This is the solution to Quiz 3

A = {{1},{2},{-3}}; B = {{2,-1,3}};

A.B//MatrixForm

B.A//MatrixForm

This is Problem 3(a) on page 66.

A = {{0,0,0,0},{1,0,0,0},{-1,2,0,0},{2,4,7,0}}

A//MatrixForm

A.A//MatrixForm

MatrixPower[A,2]//MatrixForm

A.A.A//MatrixForm

A.A.A.A//MatrixForm

Note that A^2 does NOT equal A.A.....

A^2//MatrixForm

Now onto part (b) of 3 on Page 66.

B = {{-2,0,0},{0,5,0},{0,0,-7}};

B//MatrixForm

MatrixPower[B,2]//MatrixForm

MatrixPower[B,3]//MatrixForm

For[k=1,k≤10, k++,
Print[{k,MatrixPower[B,k]//MatrixForm}]
]

I*I

IdentityMatrix[{3,4}]//MatrixForm

IdentityMatrix[{4,2}]//MatrixForm

IdentityMatrix[3]//MatrixForm