linearalgebraex1.mw

Solving Linear Algebra problems using Maple.

 > restart;

 > with(LinearAlgebra);

Vectors and matrices are defined as follows.

 > x:=Vector([1,2,3]);

 > A:=Matrix([[1,2,1],[2,4,-2]]);

Matrix-vector product

 > b:=A.x;

Finding the echelon form (not unique)

 > GaussianElimination(A);

Finding the reduced row echelon form (unique)

 > ReducedRowEchelonForm(A);

Warning, does not work for matrices with parameters. Two examples:

 > B:=Matrix([[1,2,1],[2,4,h]]);

 > ReducedRowEchelonForm(B);

This is wrong for h=2.

 > C:=Matrix([[u,v],[w,z]]);

 > ReducedRowEchelonForm(C);

This is wrong for many different values of the four parameters in this matrix.

Solving a system of linear equations

Define the coefficient matrix and the right hand side, as in the following examples. Then use the linear solver.

 > F:=Matrix([[1,2,3],[3,1,2],[-1,-1,-1]]);

 > c:=Vector([1,2,3]);

 > LinearSolve(F,c);

If the solution is not unique, then Maple returns the solution in parametrized form.

 > G:=Matrix([[1,2,3],[2,1,4]]); d:=Vector([2,2]);

 > LinearSolve(G,d);

Maple uses a particular notation for variables it defines. They always start with an underscore _

You can make Maple use any name you choose, giving it as a string in the input. The above example again, with this option.

 > LinearSolve(G,d,free='t');

 >