M 341 (58180) Spring 2007Maple DemoUse the following command to load the "Linear Algebra" library package: LinearAlgebra.with(LinearAlgebra):This segment defines two vectors in 3-dimensional space, and demonstrates vector addition, scalar multiplication, computation of inner products and norms.X := <x1,x2,x3>; Y := <y1,y2,y3>; 2*X; X + Y; DotProduct(X,Y,conjugate=false); Norm(X,2,conjugate=false);

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This segment defines three matrices, and demonstrates scalar multiplication, matrix addition, matrix multiplication, and how to generate a random matrix.A := Matrix([[a,b,c],[d,e,f]]); B := Transpose(Matrix([[1,0,1],[0,-1,1]])); C := RandomMatrix(2,3); evalm( -2 * A); evalm( A + C ); evalm( A &* B);

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This segment defines a system of linear equations in x, y, and z, and solves it using the LinearSolve command.eq1 := 3*x - 2*y + 5*z = 3; eq2 := 5*x - y + 4*z = 7; eq3 := 4*x + 3*y + 6*z = -1; solve({eq1,eq2,eq3},{x,y,z});

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This segment solves the same system as above but in matrix notation (and the command LinearSolve).A := Matrix([[3,-2,5],[5,-1,4],[4,3,6]]); b := <3,7,-1>; LinearSolve(A,b);

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eq1; eq2; eq1 + eq2; solve({eq1,eq2,eq1+eq2},{x,y,z}); A := Matrix([[3,-2,5],[5,-1,4],[5,-1,4]]); b := <0,0,0>; LinearSolve(A,b);

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