Solving Matrix Equations Worksheet by Michael K. May S.J., revised by Russell Blyth with(LinearAlgebra):

The basic objectives are: 1) Learn to use Maple to multiply matrices and vectors. 2) Learn to use Maple to solve Matrix-vector equations. 3) To complete an extended exercise.

We want to change our point of view. So far we have been focused on solving systems of linear equations and have manipulated matrices to perform that task. In this section we consider the equivalent matrix equation and how to solve it directly. Before we can talk about solving matrix equations we need to be able to multiply a matrix and an appropriately sized vector. We start by defining a matrix A and a vector X of appropriate size so that the product AX is defined. (The product AX of an m by n matrix A with the vector X is only defined if X is an n-vector.) A := Matrix(3,4,[[1, 2, 1, 3], [-5, 7, 2, 2],[ 13, 4, 4, 3]]); X := Vector(4, [1, 3, -2, 4]);

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

Recall that we can create the same matrix and vector using the angle bracket constructor. A1 := <<1, -5, 13> | <2, 7, 4> | <1, 2, 4> | <3, 2, 3>>; X1 := <1, 3, -2, 4>;

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

Now we want to compute the product. Maple uses . as the symbol for the noncommutative product of matrices. B := A.X;

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

Maple also lets you use commands for the operations. The command to multiply a matrix followed by a vector is MatrixVectorMultiply. There are similar commands for a vector and a matrix as well as for the product of two matrices. MatrixVectorMultiply(A,X);

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

Recall that the product AX can be thought of as a linear combination of the columns of A with the scalars used being the entries of X. If we compute this linear combination, we should get the same result. Column(A,1)*X[1]+Column(A,2)*X[2]+Column(A,3)*X[3]+Column(A,4)*X[4];

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

Note that multiplication of a matrix by a vector is not commutative. In fact in our case, X.A is not even defined. X.A;

Error, (in LinearAlgebra:-VectorMatrixMultiply) invalid input: LinearAlgebra:-VectorMatrixMultiply expects its 1st argument, v, to be of type Vector[row] but received Vector[Column]( 1..4, [... unable to display content ...] )

VectorMatrixMultiply(X,A);

Error, (in LinearAlgebra:-VectorMatrixMultiply) invalid input: LinearAlgebra:-VectorMatrixMultiply expects its 1st argument, v, to be of type Vector[row] but received Vector[Column]( 1..4, [... unable to display content ...] )

Sometimes we want to put two matrices (or a matrix and a vector) together into a larger matrix. We can do this with the angle bracket constructor, using a comma to put matrices on top of each other and a vertical bar to put them next to each other. <A|B>; <A,Transpose(X)>;

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

1) Use the commands RandomMatrix and RandomVector to create a random 4 by 5 matrix named Mat1 and a 5-vector named Vec1. Compute the product Mat1 . Vec1, assigned to a 4-vector named Vec2. 2) Augment Mat1 by Vec2 to create a 4 by 6 matrix. (Read carefully:) Stack Vec1 on top of Mat1 to create a 5 by 5 matrix.

Having computed B = AX, we want to shift the focus: given the matrix A and the vector B, solve for X in the matrix equation AX = B. The first method is to make an augmented matrix from A and B, then use Gaussian elimination to produce a matrix in echelon form. We then use back substitution to find the general solution to the matrix equation. C1 := <A|B>; C1a := GaussianElimination(C1); gensol1 := BackwardSubstitute(C1a);

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

Here _t[1] is a parameter that can take any value. To get back to our original X, we need to set _t[1] equal to 4. eval(gensol1,_t[1]=4);

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

A slight variation of the method above is to perform Gauss-Jordan elimination before back substitution. C1b := ReducedRowEchelonForm(C1); gensol2 := BackwardSubstitute(C1b);

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

A third option is to use the linsolve command that we saw in the previous worksheet. gensol3 := LinearSolve(A,B);

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

A fourth method notes that the general solution to the equation AX = B is any vector of the form tv+nv, where tv is a particular solution to the equation (a translation vector), and nv is any vector in the null space of A. The Maple command nullspace(A) returns a basis for the nullspace of A. (A basis of a vector space is a spanning set of minimal size.) NullSpace(A);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtb0dGJTYzUSJ8ZnJGKC8lJWZvcm1HUSdwcmVmaXhGKC8lJmZlbmNlR1EldHJ1ZUYoLyUqc2VwYXJhdG9yR1EmZmFsc2VGKC8lJ2xzcGFjZUdRLnRoaW5tYXRoc3BhY2VGKC8lJ3JzcGFjZUdGOy8lKXN0cmV0Y2h5R0Y1LyUqc3ltbWV0cmljR0Y4LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGKC8lJXNpemVHUSMxMkYoLyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYoLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GKC1GJDYjLUYkNiUtRi02M1EiW0YoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUUZURlctRiQ2Iy1JJ210YWJsZUdGJTYmLUkkbXRyR0YlNiMtSSRtdGRHRiU2Iy1JI21uR0YlNjlRKiZtaW51czs0M0YoLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR0ZTLyUlYm9sZEdGOC8lJ2l0YWxpY0dGOC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdGVi8lK2JhY2tncm91bmRHRlkvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjUvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdGUC8lKm1hdGhjb2xvckdGVi8lL21hdGhiYWNrZ3JvdW5kR0ZZLyUrZm9udGZhbWlseUdGXHAvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYoLyUpbWF0aHNpemVHRlMtRmFvNiMtRmRvNiMtRmdvNjlRKiZtaW51czs5OUYoRmpvRl1wRl9wRmFwRmNwRmVwRmdwRmlwRltxRl1xRl9xRmFxRmNxRmVxRmdxRmlxRltyRl1yRl9yRmFyRmNyRmZyLUZhbzYjLUZkbzYjLUZnbzY5USQyMzhGKEZqb0ZdcEZfcEZhcEZjcEZlcEZncEZpcEZbcUZdcUZfcUZhcUZjcUZlcUZncUZpcUZbckZdckZfckZhckZjckZmci1GYW82Iy1GZG82Iy1GZ282OUZHRmpvRl1wRl9wRmFwRmNwRmVwRmdwRmlwRltxRl1xRl9xRmFxRmNxRmVxRmdxRmlxRltyRl1yRl9yRmFyRmNyRmZyLUYtNjNRIl1GKC9GMVEocG9zdGZpeEYoRjNGNkY5L0Y9UTJ2ZXJ5dGhpbm1hdGhzcGFjZUYoRj5GQEZCRkVGSEZKRkxGTkZRRlRGVy1GLTYzUSJ8aHJGKEZfdEYzRjZGOUZhdEY+RkBGQkZFRkhGSkZMRk5GUUZURlc3Iy1fRilJLG1wcmludHNsYXNoR0YoNiQ3IzwjLUknUlRBQkxFR0YoNiUiKDdHRCUtSSdNQVRSSVhHRig2IzcmNyMhI1Y3IyEjKio3IyIkUSM3IyIiIiZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0YqNiNJJ2NvbHVtbkdGKDcjPCMtRl12NiMvSSQlaWRHRihGYHU=

3) Find a basis of the null space of the matrix Mat1 you created above. 4) Solve the matrix-vector equation (Mat1)(X) = Vec2 by reducing an augmented matrix. 5) Solve the matrix-vector equation (Mat1)(X) = Vec2 by using the linsolve command.

For these exercises we will work with a fixed matrix A and a fixed vector B. Let A = 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 and B = 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. Exercises: 6) Compute the rank of A and determine the number of free variables in the system AX = 0. A := Matrix(<< 17 | -6 | 13 | 27 | 64 | 19 >, < 4 | -6 | -33 | 25 | 7 | 9 >, < 55 | -24 | 6 | 106 | 199 | 66 >, < 89 | -36 | 32 | 160 | 327 | 104 >>);

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

Find a basis for the nullspace of A. (Name the vectors of your basis W1, W2, ...) How could you have predicted the size of the basis? W:=NullSpace(A); W1:= W[1]; W2:= W[2]; W3 := W[3]; W4 := W[4];

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

By inspection, find a vector X0 such that (A)(X0)=B. X0 := <1,0,0,0,0,0>; A.X0;

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

Show that any vector of the form X0 + a1*W1 + a2*W2 + ... is a solution to the equation AX = B. X := X0 + a1*W1 + a2*W2 + a3*W3 + a4*W4; A.X;

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