Chapter 8, Problem 58RE

a.

To determine

Product of matrix AB

Answer to Problem 58RE

Product of matrix $AB\text{=}\left[7\text{ 7 2}\right]$

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}2\text{ 3}\\ \text{8 -1}\\ \text{0 2}\end{array}\right],B=\left[\begin{array}{l}4\\ 1\end{array}\right]$

Dimension of matrix A is $3\times 2$ and size of matrix B is $2\times 1$ as the number of column of matrix A is equal to number of row of matrix B therefore product AB is possible.

And size of matrix AB will be $3\times 1$

  $\begin{array}{l}AB=\left[\begin{array}{l}2\text{ 3}\\ \text{8 -1}\\ \text{0 2}\end{array}\right]\left[\begin{array}{l}4\\ 1\end{array}\right]\\ =\left[2\times 4+3\times 1\text{ 8}\times \text{4-1}\times 1\text{ 0}\times \text{4+2}\times \text{1}\right]\\ \text{=}\left[7\text{ 7 2}\right]\end{array}$

Therefore. Product of matrix $AB\text{=}\left[7\text{ 7 2}\right]$

b.

To determine

Product of matrix BA

Answer to Problem 58RE

Product of matrix BA is not possible.

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}2\text{ 3}\\ \text{8 -1}\\ \text{0 2}\end{array}\right],B=\left[\begin{array}{l}4\\ 1\end{array}\right]$

Dimension of matrix A is $3\times 2$ and size of matrix B is $2\times 1$ as the number of column of matrix B is not equal to number of row of matrix B therefore product AB is possible.

Therefore product BA is not possible.

c.

To determine

Square of the matrix.

Answer to Problem 58RE

Square of the matrix $A^2$ is not possible.

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}2\text{ 3}\\ \text{8 -1}\\ \text{0 2}\end{array}\right],B=\left[\begin{array}{l}4\\ 1\end{array}\right]$

Dimension of matrix A is $3\times 2$ so it is not square matrix

Therefore square of the matrix $A^2$ is not possible.