M 341 (Spring 2007) Example 7, Section 2.1, p.76

restart:

Load in the LinearAlgebra library package.

with(LinearAlgebra):

We define the matrix A, which is the augmented coefficient matrix of the Example. We then compute its reduced row echelon form with the suitable Maple command.

A:=Matrix([[ 3, 1, 7, 2, 13], [ 2,-4,14,-1,-10], [ 5,11,-7, 8, 59], [ 2, 5,-4,-3, 39]]); ReducedRowEchelonForm(A);

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We solve the system using the LinearSolve command. Note Maple's notation for a parameter.

CoeffMatrix := SubMatrix(A,1..4,1..4); RightHandSide := SubMatrix(A,1..4,5..5); LinearSolve(CoeffMatrix,RightHandSide);

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Lastly, we perform row reductions on the augmented coefficient matrix to bring it to row reduced echelon form. Note that we can perform two operations in one line (assignment).

temp:=eval(A); temp:=RowOperation(RowOperation(temp,[1,2],-1),[4,2],-1); temp:=RowOperation(RowOperation(temp,[2,1],-2),[3,1],-5); temp:=RowOperation(RowOperation(temp,[3,2],-1),[3,4]); temp:=RowOperation(RowOperation(temp,2,-2),[2,3],-3); temp:=RowOperation(temp,[3,2],-9); temp:=RowOperation(temp,3,-1/182); temp:=RowOperation(temp,[1,2],-5); temp:=RowOperation(RowOperation(temp,[1,3],97),[2,3],-20);

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