Other such commands are “zeros” (for zero matrices) and “magic” (type help zeros and help magic for more information). Command “eye” generates the identity matrix (try typing eye(3)). 1 1 0 2 1 1 rref 1 0 1 0 1 1 We read from this that x 1 1. There are several MATLAB commands that generate special matrices.Ĭommand “rand” generates matrices with random entries (rand(3,4) creates a 3x4 matrix with random entries). We know how to solve this put the appropriate matrix into reduced row echelon form and interpret the result. Type:Ĭommand “det” computes determinants (we will learn more about determinants shortly). Typeįor more information on how to use the command.Ĭommand “inv” calculates the inverse of a matrix. To save your work, you can use command “diary”. You can also get help using command "doc". TypeĪnd you will get as a result a number of MATLAB commands that have to do with row echelon forms. Sometimes we do not know the exact command we should use for the problem we need to solve. To find out more about command "help", typeĬommand "help" is useful when you know the exact command you want to use and you want to find out details on its usage. For example, type:Īnd you will get information on the usage of "rref". Example 1 Use augmented matrices to solve each of the following systems. ![]() It shows you how MATLAB commands should be used. (Can we always use this method to solve linear systems in MATLAB? Experiment with different systems.)Ĭommand "help" is a command you should use frequently. ![]() This command will generate a vector x, which is the solution of the linear system. The symbol between matrix A and vector b is a “backslash”. You can also solve the same system in MATLAB using command You now need to use command “rref”, in order to reduce the augmented matrix to its reduced row echelon form and solve your system:Ĭan you identify the solution of the system after you calculated matrix C? An (augmented) matrix D is row equivalent to a matrix C if and only if D is obtained from C by a finite number of row operations of types (I), (II), and (III). ![]() You have now generated augmented matrix Aaug (you can call it a different name if you wish). In order to solve the system Ax=b using Gauss-Jordan elimination, you first need to generate the augmented matrix, consisting of the coefficient matrix A and the right hand side b: To solve AX B for X, we form the proper augmented matrix, put it into reduced row echelon form, and interpret the result. To generate a column vector b (make sure you include the prime ’ at the end of the command). This command generates a 3x3 matrix, which is displayed on your screen.
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