linsolve.html

Whenever performing matrix operations (linear algebra), first load the linalg library of commands:

> with( linalg ) :

1. Using the gaussjord command:

To define an augmented matrix :

Note: The above is an augmented matrix - the first 3 columns denote the coefficient matrix A , and the 4th column denotes the constant vector b .

> C := matrix( [ [ 4, –2, 2, –6], [ 20, –12, 3, –52], [ –16, 14, 7, 66] ] ) ;

Solve the augmented matrix with the gaussjord command:

> soln := gaussjord( C ) ;

As long as the first n x n portion is the identity matrix, then the last column represents the solution

Store the solution (the 4th column of "soln") in vector xvec :

> xvec := col( soln, 4 ) ;

You may then reference the entries of the solution using their subscripts:

> xvec[1] ;

> xvec[2] ;

> xvec[3] ;

To convert the solution vector to decimal form, use:

> evalf( evalm (xvec) ) ;

Alternatively, if you use decimal points on the entries of A , then all calculations will be done in decimal form.

2. Using the linsolve command:

To solve the matrix problem:

Note: in the above problem, the coefficient matrix A and the constant vector b are:

Define the coefficient matrix and the constant vector .

> A := matrix( [ [ 4, –2, 2], [ 20, –12, 3 ], [ –16, 14, 7 ] ] ) ;

> b := vector( [ -6, -52, 66 ] ) ;

Use linsolve to solve the system Ax = b , and name the solution vector xvec:

> xvec := linsolve( A, b ) ;

To convert the soution vector to decimal form, use:

> evalf( evalm( xvec ) ) ;

Alternatively, if you use decimal points on the entries of A , then all calculations will be done in decimal form.