Let A = * 1 1 1 0 2 1+ , B = * 2 0 1 3+ , and C = 0 2 3 1 1 0 . For each of the

Chapter 10, Problem 10

(choose chapter or problem)

Let \(\mathbf{A}=\left[\begin{array}{rrr}1 & 1 & -1 \\ 0 & -2 & 1\end{array}\right], \mathbf{B}=\left[\begin{array}{rr}-2 & 0 \\ 1 & 3\end{array}\right]\), and \(\mathbf{C}=\left[\begin{array}{rr}0 & -2 \\ 3 & 1 \\ 1 & 0\end{array}\right]\)

For each of the following, determine whether the indicated product exists, and compute it if it does.

a. AB

b. BA

c. \(\mathbf{A}^{2}\)

d. BC

e. CB

f. \(\mathbf{B}^{2}\)

g. \(\mathbf{B}^{3}\)

h. \(\mathbf{C}^{2}\)

i. AC

j. CA

Text Transcription:

A = [ 1 1 −1 0 −2 1] , B = [ −2 0 1 3] , and C =[ 0 −2 3 1 1 0 ]

A^2

B^2

B^3

C^2