- ants (we will learn more about deter
- %If the price of the items are denoted by the matrix p, then the linear relationship would be Cp=p %or equivalently Cp-p= Cp-Ip= (C-I)p=0 (where I is an identity matrix with 1's on the diagonal and o's everywhere else.
- MATLAB: Augmented Matrices In this activity you will define an augmented matrix, find the number of pivot variables in the reduced system, and find the number of free variables in the solution to the linear system of equations
- An augmented matrix can be defined as an equivalent representation with respect to a system of linear equations. In the derived set of equation, when an equation is multiplied by a constant and is added to another equation, then the resultant solution consisting set of a new system is the same as the previous one
- Step by step output of Gauss Jordan in MatLab | Reduced Echelon form of Augmented matrix in MatLab
- It executes EROs to convert this augmented matrix into an upper triangular form. It uses back-substitution to solve for the unknowns in x. Example. Use a 2 x 2 system, the augmented matrix would be: Then, EROs are used to get the augmented matrix into an upper triangular form: So, it is simply to replace a 21 with 0. Here, the primes indicate.

The matrix to the left of the bar is called the coefficient matrix. 15111 0312 2428 −− − 6. Solving an Augmented Matrix To solve a system using an augmented matrix, we must use elementary row operations to change the coefficient matrix to an identity matrix. Form the augmented matrix 15111 0312 2428 −− − Interchange rows 2 and 3. **Augmented** **matrix**: Thus, x= 2, y = 3 and z = -1. This is the required solution which is same as that obtained from Gauss elimination method's **MATLAB** code. If you have any questions regarding Gauss elimination method, its **MATLAB** program code, or its mathematical derivation, bring them up from the comments ** The calculator will find the row echelon form (RREF) of the given augmented matrix for a given field, like real numbers (R), complex numbers (C), rational numbers (Q) or prime integers (Z)**. You can enter a matrix manually into the following form or paste a whole matrix at once, see details below Form the augmented matrix and use rref to solve each of the following systems from Part 10 of this Tutorial: x - 2y + z = 0 2y - 8z = 8 -4x + 5y + 9z = -

$\begingroup$ I'm not necessarily asking how to add a column, but rather, How to add a column intuitively. I use Mathematica in my classroom and often row operations/Gaussian Elimination is taught before the transpose. So augmenting a matrix with a double transpose or with the Flatten command is confusing to students. MATLAB's method is much, much more intuitive This video shows how to transform and augmented matrix to row echelon form to solve a system of equations.http://mathispower4u.yolasite.com/http://mathispowe..

- To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix
- This augmented matrix is easily entered in Matlab's workspace. >> A=[1 1 1 -6;1 0 -2 4;2 1 -1 18] A = 1 1 1 -6 1 0 -2 4 2 1 -1 18 Matlab's rref command will now be used to place matrix A in reduced row echelon form. >> R=rref(A) R = 1 0 -2 0 0 1 3 0 0 0 0 1 Thus, the reduced row echelon form of the augmented matrix 7 is 1 0 −2 0 0 1 3 0 0.
- Q1: No. Here's a counter-example: >> A = eye(4)*1e-300 A = 1.0e-300 * 1.0000 0 0 0 0 1.0000 0 0 0 0 1.0000 0 0 0 0 1.0000 >> rank(A) ans = 4 >> >> rank([A, ones(4, 1)]) ans = 1 >>
- Now, by augmenting the matrix with the vector on the right and using row operations, this equation can easily be solved by hand. However, if our system did not have nice integer entries, solving the system by hand using row reduction could become very difficult. MATLAB provides us with an easier way to get an answer
- ation on augmented matrices to solve a linear system and calculate the matrix inverse. These techniques are mainly of academic interest, since there are more efficient and numerically stable ways to calculate these values. Create a 3-by-3 magic square matrix. Add an additional column to the end of the matrix

Problem 2 Use MATLAB to construct the augmented matrix [A b) and then perform using row reductionhte rref() function. Write out your reduced matrix and identify the free and basic variables of the system An augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable

(a) Enter it into MATLAB as an (augmented) matrix named B. (b) Use elementary row operations (as in part 5 of the guide) to reduce it to row echelon form. (c) Continue using elementary row operations to get to reduced row echelon form. (d) Re-enter the original matrix into MATLAB and use the rref command to instantly get the reduced row echelon. ** (This is called the Augmented Matrix) Identity Matrix**. The Identity Matrix is the matrix equivalent of the number 1: A 3x3 Identity Matrix. It is square (has same number of rows as columns), It has 1s on the diagonal and 0s everywhere else. It's symbol is the capital letter I Gauss-Jordan Method is a popular process of solving system of linear equation in linear algebra. This method solves the linear equations by transforming the augmented matrix into reduced-echelon form with the help of various row operations on augmented matrix. Gauss-Jordan method is an elimination maneuver and is useful for solving linear equation as well as for determination of inverse of a.

This video explains how to determine the solution to a system of equations from an augmented matrix in reduced row echelon form.http://mathispower4u.co The rank of a matrix is the dimension of the span of its columns. The coefficient matrix has fewer columns than the augmented matrix. So, the answer to your first question is no. I don't understand the second one * Gauss-Jordan Method is a popular process of solving system of linear equation in linear algebra*. This method solves the linear equations by transforming the augmented matrix into reduced-echelon form with the help of various row operations on augmented matrix. Gauss-Jordan method is an elimination maneuver and is useful for solving linear equation as well a Suppose now you want to solve a system of matrices by getting the augmented matrix in reduced row-echelon form but you don't want to do all that work on the previous page. The rref command does this in MATLAB. For example if I put in the augmented matrix (corresponding to a system of linear equations) for the previous page's problem The above source code for Gauss elimination method in MATLAB can be used to solve any number of linear equations. The order of augmented matrix relies on the number of the linear equations to be solved by using this method. As the matrix element data are embedded within the source code, the user doesn't need to give input to the program

3. Use MATLAB (A \ B) to solve the system of equations given (as augmented matrix) below. Change the coefficientsai to 6.00 instead of 6.03 and a33 to 1.00 instead of 0.987; then re-solve the equations. How do the answers change? Is the system Sill-conditioned? Explain The augmented matrix approach is another method designed for reducing numerical ill-conditioning issues. According to this method, the measurement residuals are considered as variables and included in the SE formulation as equality constraints (together with the other constraints already seen in the Equality-Constrained WLS) Augmented Lagrange Multiplier (ALM) Method [inexact ALM - MATLAB zip] Usage - The most basic form of the inexact ALM function is A = inexact_alm_mc(D) , where D is the incomplete matrix defined in the MATLAB sparse matrix format and the output A is a structure with two components - A.U and A.V (the left and right singular vectors scaled.

- Fig 3. Typical workflow for training a network using an augmented image datastore (from [7]). For a complete example of an image classification problem using a small dataset of flower images, with and without image data augmentation, check my MATLAB File Exchange contribution [8]
- ation. To execute Gaussian eli
- ation algorithm is divided into forward eli
- How to add in row swappinghttps://youtu.be/BCfjq8882D
- This video is provided by the Learning Assistance Center of Howard Community College. For more math videos and exercises, go to HCCMathHelp.com
- augmented coefficient matrix file. The augmented coefficient matrix file contains the coefficient matrix in rows and columns with the right hand side vector appended as the (n+1)th column, where n is the number of equations in the system. For example, the augmented coefficient matrix for the quarry problem would look like 0.10 0.55 0.50 2
- For part of my Statics homework, I have to create a MATLAB function that will take n forces acting on a system and turn them into an nx3 matrix. Yes, the ns are intentional, the amount of rows is supposed to change with the amount of forces

- Question: This Is Linear Algebra MATLaB 1.8 Augmented Matrices X_1+3x_2 -2x_3+2x_5=0 2x_1+6x_2-5x_3 -2x_4+4x_5-3x_6=-1 X_3+5x_4+3x_6=1 X_1+3x_2+4x_4+2x_5+9x_6=3 Create A Coefficient Matrix A Create The Column B Of Constants. Remember To Create A Column Matrix , The Rows Are Separated By Semicolons. Create The Augmented Matrix [A| B]. Store This Matrix In Ab..
- In the case when the augmented matrix in RREF tells us that there is a solution, we can often say more about the solution set as we will see next. The case of multiple solutions. Suppose that the augmented matrix does not have a row that contains all \(0\)'s except the right-most entry
- Create a Matrix in MATLAB Define a Matrix. Let's start by defining matrices. The first thing to know is that you can separate rows by semi-colons (;) and that you define rows by just placing elements next to one another. Then, use square brackets to mark the beginning and the end of your matrix. For example, let's say you have the following.
- In previous versions of MATLAB ®, the augmented matrix was used by sparse linear equation solvers, \ and /, for nonsquare problems. Now, MATLAB calculates a least-squares solution using the qr factorization of A
- imization on unstructured polygonal finite elements. To solve the nonlinear elasticity problem, we implement a Newton-Raphson scheme, which can.
- If i have a matrix like this: 2 1 4 6 2. 9 4 6 1 2. 5 3 2 8 3. 7 2 1 9 3. 7 1 8 2 4. 3 5 4 1 2. then i want to stick on a vektor contain of 1 in the beginning of that matrix. so it'll be like this: I'm a student just learning how to use MATLAB... but I'm pretty sure you can use the horzcat function to do it easily. Matlab has.

- Though your activity may be recorded, a page refresh may be needed to fill the banner. 0/1 MATLAB: Inverse of a Square Matrix In this activity you will find the inverse of a square matrix two ways, using an augmented matrix and using the inv) command. %Create the square matrix A
- e if a system of equations had a solution. The poster wasn't (at least yet) concerned with what the solution was
- Matlab Multiple choice Questions: We have listed here the best Matlab MCQ Questions for your basic knowledge of Matlab. This Matlab Test contains 25 multiple Choice Questions. You have to select the right answer to every question
- This is called an augmented matrix: the grid containing the coefficients from the left-hand side of each equation has been augmented with the answers from the right-hand side of each equation. The entries of (that is, the values in) the matrix correspond to the x -, y - and z -values in the original system, as long as the original system is.
- How would i go about solving a system of equation with use of the rref in Matlab?? eg. 4x1 + 4x2 - 4x3 - 2x4 + 5x5 = -5-x1 - 5x2 + 9x3 - 2x4 - 5x5 =1
- g Row Operations on a Matrix. Now that we can write systems of equations in augmented matrix form, we will exa

Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchang Since MATLAB specializes in matrices, you do not need to add any packages, and anything you enter will be assumed by default to be a matrix. So, using a previous example, enter >>A1=[2-54-3;1-215;1-4610] or, to type something that looks more like a matrix, MATLAB will allow you to do >>A=[2-54-3 1-215 1-4610] %% Math 240 Matlab Project 1 % Spring 2021 % % Section [0213] % % Author: [Chimaobi Martins Okorie] % % Group members: [Chimaobi Martins Okorie] %% %% Problem 1 % (a) Enter it into MATLAB as an (augmented) matrix named A. A=[1,4,0,13;-1,-3,-1,-8;-4,-16,1,-59] %% % (b) Use elementary row operations (as in part 5 of the guide) to reduce it to row.

Problem 2 Use MATLAB to construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced matrix and identify the free and basic variables of the system * After user selects to add or withdraw money, it doesn't change the balance in the matrix*. It stays the same as the original data, is there anyway to change one matrix by augmenting? Is the ATM Machine designed in MATLAB? After importing excel data and processing, make sure to write the new data back to excel. Check if you are getting any. Row Operations. Now that we can write systems of equations in augmented matrix form, we will examine the various row operations that can be performed on a matrix, such as addition, multiplication by a constant, and interchanging rows.. Performing row operations on a matrix is the method we use for solving a system of equations Description. S = spaugment(A,c) creates the sparse, square, symmetric indefinite matrix S = [c*I A; A' 0].The matrix S is related to the least-squares proble

A square matrix with rank equal to the number of rows and columns is said to be full rank. Full rank matrices have all non-zero pivots. When a row or column is a linear combination of others rows or columns, then a pivot will be zero and the rank is reduced. MATLAB has a rank function which takes a matrix as input. Solution Requirements fo 2.6 MATLAB: Inverse of a Square Matrix LAB ACTIVITY 2.6.1: MATLAB: Inverse of a Square Matrix This tool is provided by a third party. Though your activity may be recorded, a page refresh may be needed to fill the banner. 0 / MATLAB: Inverse of a Square Matrix In this activity you will find the inverse of a square matrix two ways, using an augmented matrix band using the inv( ) command The attached matlab code simulates data from this state space model and subsequently runs through a kalman filter with an augmented state space vector, X(t). My problem is, that the filtered (and the predicted) process differs substantially from the true latent process. This can be seen from the attached figure as well

- d that its entries will change as the algorithm progresses. We initialize M
- ation to obtain the reduced row echelon form (b) For each row-reduced augmented matrix, state if the corresponding system of equations has no solution, a unique solution, or infinitely many solutions 1 0 0 3 0 0 0 -1 0.
- Browse other questions tagged matrices matlab control-theory optimal-control linear-control or ask your own question. The Overflow Blog Vote for Stack Overflow in this year's Webby Awards
- % OUTPUT solution vector x of equation Ax=b; % upper triangular matrix An after n-1 steps % lower triangular matrix Ln containing mjl % number of row exchanges % Notice that the function written here is not very % efficient with respect to saving memory: Typically % we would not have to define extra matrices Ln and An % for this procedure
- Matlab gives you a solution anyway! and a warning. x = A\b % categories: Linear algebra Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 3.364312e-018. x = 1.0e+016 * 1.8014 -1.8014 -1.8014 Published with MATLAB® 7.1

Matlab comes with a rreffunction for row reducing matrices. For Octave you can download rref.mfrom our web site, and place it into your working directory. Provided an augmented matrix A, type > rref(A) which produces a REF. 3.1 General solutions Suppose that the following REF is obtained. 2 4 1 0 5 1 0 1 1 4 0 0 0 0 3 MATLAB: Augmented Matrices In this activity you will define an augmented matrix, find the number of pivot variables in the reduced system, and find the number of free variables in the solution to the linear system of equations. Consider the linear system of equations: 2xty = 3 x+ 2y =

(a) Follow the instructions in the introduction on how to enter the augmented matrix A I 3, put it in reduced row echelon form, and then extract the inverse matrix A 1. (b) Now let MATLAB compute the inverse of Adirectly using the inv command. Make sure your answer coincides with the previous part. 3 The Augmented Lagrange Multiplier Method for Matlab code of all algorithms discussed are avail- matrices with dimensions as small as m = 800, the algorithm has to run 8 hours on a typical PC. To alleviate the slow convergence of the iterative thresholding method [22] Matlab program for 3D DOA estimation of L-shaped array based on augmented matrix pencil. 2018-08-14. 1 0 0. no vote. Other. 1 Points Download Earn points. In the spatial DOA estimation, the array element arrangement of the surface type is needed. This program is set as the L-shape distribution of 8 + 8 microphone, and the DOA estimation can be.

Use the octave/MatLab operation rref to row reduce matrices. Suppose you want to row reduce (Use Gaussian Elimination) the following augmented matrix: 0 @ 1 2 1 0 0 2 8 8 5 0 5 10 1 A You can type: B=[1 -2 1 0; 0 2 -8 8; 5 0 -5 10] or B=[1,-2, 1, 0; 0, 2, -8, 8; 5, 0, -5, 10] Then type: rref(B) which will spit out this matrix: 1 0 0 1 0 1 0 0 0. A matrix is a two-dimensional array of numbers. In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row. For example, let us create a 4-by-5 matrix a An augmented matrix in reduced row echelon form corresponds to a solution to the corresponding linear system. Thus, we seek an algorithm to manipulate matrices to produce RREF matrices, in a manner that corresponds to the legal operations that solve a linear system. We already encountered row operations, and these will be th

From each of these row-reduced versions of the augmented matrices, one can read oﬀ the rank of the coeﬃcient matrix as well as the rank of the augmented matrix. Applying Theorem 1.2 to each of these tells us the number of solutions to expect for each of the corresponding systems. We summarize our ﬁndings in the tabl Finally, we subtract the third row from the fourth to obtain the augmented matrix of an upper-triangular system, A~(7) = 2 6 6 4 1 2 1 1 5 0 4 1 7 1 0 0 2 1 1 0 0 0 1 3 3 7 7 5: Note that in a matrix for such a system, all entries below the main diagonal (the entries where the row index is equal to the column index) are equal to zero. That is. Making a augmented matrix in matlab, and reduced row echelon form. 0. Reduced row echelon form of binary matrix in MatLab. 6. Solving a simple matrix in row-reduced form in C++. 1. transformation matrix of reduced row echelon form. 2. Math.Net system of linear equations with a 0 value in solution. 1 (which also corresponds to the linear system in matrix-vector form, A~x = ~b), we may use the Matlab \backslash command: x = A \ b Use this command to solve for the values x 1;:::;x 8. After solving for the vector ~x, you can have Matlab check the answer by entering b - A*x and seeing whether the result is all zero Let us see how to solve a system of linear equations in MATLAB. Here are the various operators that we will be deploying to execute our task : \ operator : A \ B is the matrix division of A into B, which is roughly the same as INV(A) * B.If A is an NXN matrix and B is a column vector with N components or a matrix with several such columns, then X = A \ B is the solution to the equation A * X = B

In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.. Given the matrices A and B, where = [], = [], the augmented matrix (A|B) is written as (|) = [].This is useful when solving systems of linear equations This reduces the augmented matrix to MATLAB MATRIX OPERATIONS To obtain the LU-factorization of a matrix, including the use of partial pivoting, use the Matlab command lu. In particular, [L,U,P]=lu(X) returns the lower triangular matrix L, upper triangula

Substitute this value into the first equation to obtain x = -I. Substituting these values into the third equation gives -I + 10 = c, which is satisfied only if c = 9. Thus a solution exists if and only if c = 9. (b) The coefficient matrix and the augmented matrix for this problem are. In MATLAB, enter the array A = [ 1 , 1; 1, 2 ; 1, 5) To solve a system of equations using matrices, we transform the augmented matrix into a matrix in row-echelon form using row operations. For a consistent and independent system of equations, its augmented matrix is in row-echelon form when to the left of the vertical line, each entry on the diagonal is a 1 and all entries below the diagonal are. This article covers how to create matrices, vectors, and cell arrays with the programming software MATLAB. Since MATLAB is a program offering endless possibilities, being able to understand the basics will lead to the ability to write more complex codes later on. No previous knowledge of MATLAB is required for these instructions A variant of Gaussian elimination called Gauss-Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I] Likewise, the horizontal length of the matrix (number of columns) equals the length of the unknowns vector. It is common to write the system Ax=b in augmented matrix form : The next few subsections discuss some of the basic techniques for solving systems in this form. More advanced techniques are saved for later chapters

Linear Algebra Using Matlab MATLAB is short for \MATrix LABoratory. It provides a friendly environment for manipu-lating matrices and also contains a large number of built routines that make matrix algebra simple. Basic Matrix Commands If M is a matrix in MATLAB, then M(2,3) denotes the entry in the second row, third column of M. For example I do believe that using an augmented coefficient matrix is very worthwhile, very often, to get variables out of the way temporarily, and for dealing with many equations in many unknowns: and even for $3\times 3$ systems when the associated augmented coefficient matrix has mostly non-zero entries. It just makes more explicit (and easier to. MATLAB is an abbreviation for matrix laboratory. While other programming languages mostly work with numbers one at a time, MATLAB® is designed to operate primarily on whole matrices and arrays. All MATLAB variables are multidimensional arrays, no matter what type of data. A matrix is a two-dimensional array often used for linear algebra An augmented matrix is a combination of two matrices, and it is another way we can write our linear system. When written this way, the linear system is sometimes easier to work with Augmented Matrices and Row Operations. Solving equations by elimination requires writing the variables x, y, z and the equals sign = over and over again, merely as placeholders: all that is changing in the equations is the coefficient numbers.We can make our life easier by extracting only the numbers, and putting them in a box

Solve Using an Augmented Matrix, Write the system of equations in matrix form. Find the reduced row echelon form of the matrix. Tap for more steps... Perform the row operation on (row ) in order to convert some elements in the row to . Tap for more steps.. The command eye(n) used here creates an n×n matrix with ones on the diagonal and zeros elsewhere. Use MATLAB to row-reduce the augmented matrix [C - I | 0], and write down the general solution to (C - I)p = 0. What are highest- and lowest-priced commodities in this model community? List the inhabitants in order of income, from lowest to highest

A permutation matrix has the rows of an identity matrix, but in a different order. MATLAB often does row exchanges for performance reasons even when there are no zero pivots. Thus, for some matrices, MATLAB will not produce the same and matrices as one would derive from a manual elimination process Sal solves a linear system with 3 equations and 4 variables by representing it with an **augmented** **matrix** and bringing the **matrix** to reduced row-echelon form. If you're seeing this message, it means we're having trouble loading external resources on our website

Use the economy-size QR decomposition of a coefficient matrix to solve the linear system Ax = b. Create a 10-by-5 coefficient matrix by using the first five columns of magic(10). For the right-hand side of the linear equation Ax = b, use the row sums of the matrix The inverse of a matrix: A special square matrix is the identity matrix. This matrix has 1's seating on each place of its main diagonal, and zero everywhere else. For example the 3X3 identity matrix is: Now we can pose the following problem: If a nXn square matrix A is known, can we find a matrix A-1 so that . A A-1 = identity matrix The goal when solving a system of equations is to place the augmented matrix into reduced row-echelon form, if possible. There are three elementary row operations that you may use to accomplish placing a matrix into reduced row-echelon form. Each of the requirements of a reduced row-echelon matrix can satisfied using the elementary row operations Vectors and Matrices in MATLAB . MATLAB is written to work with vectors and matrices; the name MATLAB is short for Matrix Laboratory. A matrix looks like a table with rows and columns; an m by n (or m x n) matrix has m rows by n columns (these are the dimensions of the matrix). Vector

Free Matrix Row Echelon calculator - reduce matrix to row echelon form step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy So we can conclude the inverse of the matrix A is the right hand portion of the augmented matrix: A −1 = 0.0939: 0.1918-0.1469 -0.2041: 0.0612: 0.102: 0.1388-0.2816: 0.1306: Things to Note. The above explanation shows all steps. A human can usually take a few shortcuts. Also, sometimes there is already a 1 or a 0 in the correct position. MATLAB provides an easy way to determine the rank of a matrix: First define the matrix A as an array in the usual way. Then type rank (A).For example, the following MATLAB session determines the rank of the matrix given by (6.4-1). j' , »A = [3,-4,1;6,10,2;9,-7,3]; »rank(A) ans= 2 Existence and Uniqueness of Solution

Representing linear systems of equations with augmented matrices. Representing linear systems with matrices. This is the currently selected item. Practice: Represent linear systems with matrices. Next lesson. Elementary matrix row operations. Sort by: Top Voted Augmented Matrix. A matrix form of a linear system of equations obtained from the coefficient matrix as shown below. It is created by adding an additional column for the constants on the right of the equal signs (Of course, you must modify the sample MATLAB commands above to reflect the fact that the augmented matrix M will now be a 9 x 10 matrix, R should be its reduced row echelon form, and now T will be a 5 x 5 matrix of temperatures.) Larger Grids and a Little Programmin In the recently presented sparse matrix extension of MATLAB, there is no routine for sparse QR factorization. Sparse linear least-squares problems are instead solved by the augmented system method. The accuracy in computed solutions is strongly dependent on a scaling parameter δ (Note that the matrix inverse method will never work with such sets.) The matrix left-division method; solve for x by typing x = A\B. The pseudoinverse method; solve for x by typing x = pinv (A) *b. The reduced row echelon form (RREF) method. This method uses the MATLAB command rref to obtain a solution