Chapter 8.2, Problem 11E

a.

To determine

To find: $A+B.$

Answer to Problem 11E

  $A+B$ can’t be determined.

Explanation of Solution

Given information:

  $A=\left[\begin{array}{ccc}6& 0& 3\\ -1& -4& 0\end{array}\right]\text{and}B=\left[\begin{array}{cc}8& -1\\ 4& -3\end{array}\right]$

Calculations:

The order of matrix $A$ is $2\times 3$ and that of matrix $B$ is $2\times 2$ .

Since the orders of both the matrices are different, performing $A+B$ is not possible.

b.

To determine

To find: $A-B.$

Answer to Problem 11E

  $A-B$ can’t be determined.

Explanation of Solution

Given information:

  $A=\left[\begin{array}{ccc}6& 0& 3\\ -1& -4& 0\end{array}\right]\text{and}B=\left[\begin{array}{cc}8& -1\\ 4& -3\end{array}\right]$

Calculations:

The order of matrix $A$ is $2\times 3$ and that of matrix $B$ is $2\times 2$ .

Since the orders of both the matrices are different, performing $A-B$ is not possible.

c.

To determine

To find: $3A$

Answer to Problem 11E

The matrix $3A=\left[\begin{array}{ccc}18& 0& 9\\ -3& -12& 0\end{array}\right]$

Explanation of Solution

Given information:

  $A=\left[\begin{array}{ccc}6& 0& 3\\ -1& -4& 0\end{array}\right]\text{and}B=\left[\begin{array}{cc}8& -1\\ 4& -3\end{array}\right]$

Calculations:

  $\begin{array}{l}3A=3\left[\begin{array}{ccc}6& 0& 3\\ -1& -4& 0\end{array}\right]\\ =\left[\begin{array}{ccc}3\times 6& 3\times 0& 3\times 3\\ 3\times (-1)& 3\times (-4)& 3\times 0\end{array}\right]\\ =\left[\begin{array}{ccc}18& 0& 9\\ -3& -12& 0\end{array}\right]\end{array}$

d.

To determine

To find: $3A-2B$

Answer to Problem 11E

  $3A-2B$ can’t be determined.

Explanation of Solution

Given information:

  $A=\left[\begin{array}{ccc}6& 0& 3\\ -1& -4& 0\end{array}\right]\text{and}B=\left[\begin{array}{cc}8& -1\\ 4& -3\end{array}\right]$

Calculations:

  $\begin{array}{l}3A=3\left[\begin{array}{ccc}6& 0& 3\\ -1& -4& 0\end{array}\right]\\ =\left[\begin{array}{ccc}3\times 6& 3\times 0& 3\times 3\\ 3\times (-1)& 3\times (-4)& 3\times 0\end{array}\right]\\ =\left[\begin{array}{ccc}18& 0& 9\\ -3& -12& 0\end{array}\right]\end{array}$

And

  $2B=2\left[\begin{array}{cc}8& -1\\ 4& -3\end{array}\right]=\left[\begin{array}{cc}2\times 8& 2\times (-1)\\ 2\times 4& 2\times (-3)\end{array}\right]=\left[\begin{array}{cc}16& -2\\ 8& -6\end{array}\right]$

The order of $3A$ is $2\times 3$ and that of $2B$ is $2\times 2$ . Since they are different, $3A-2B$ can’t be performed.