linearalgebraex1.mw
Solving Linear Algebra problems using Maple.
Start by loading the linear algebra package
Vectors and matrices are defined as follows.
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A:=Matrix([[1,2,1],[2,4,-2]]); |
Matrix-vector product
Finding the echelon form (not unique)
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GaussianElimination(A); |
Finding the reduced row echelon form (unique)
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ReducedRowEchelonForm(A); |
Warning, does not work for matrices with parameters. Two examples:
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B:=Matrix([[1,2,1],[2,4,h]]); |
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ReducedRowEchelonForm(B); |
This is wrong for h=2.
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C:=Matrix([[u,v],[w,z]]); |
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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.
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F:=Matrix([[1,2,3],[3,1,2],[-1,-1,-1]]); |
If the solution is not unique, then Maple returns the solution in parametrized form.
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G:=Matrix([[1,2,3],[2,1,4]]); d:=Vector([2,2]); |
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.
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LinearSolve(G,d,free='t'); |