Chapter 8.2, Problem 13E

(a).

To determine

To calculate: $A+B$

Answer to Problem 13E

  $\left[\begin{array}{ccccc}5& 1& -2& 4& 4\\ -5& 10& 0& -4& -7\end{array}\right]$

Explanation of Solution

Given information: $A=\left[\begin{array}{ccccc}4& 1& -1& 3& 4\\ 1& 2& -2& -1& 0\end{array}\right],B=\left[\begin{array}{ccccc}1& 0& -1& 1& 0\\ -6& 8& 2& -3& -7\end{array}\right]$

Calculation:

To find $A+B$ , add corresponding elements of A and B

  $\begin{array}{l}A+B=\left[\begin{array}{ccccc}4& 1& -1& 3& 4\\ 1& 2& -2& -1& 0\end{array}\right]+\left[\begin{array}{ccccc}1& 0& -1& 1& 0\\ -6& 8& 2& -3& -7\end{array}\right]\\ =\left[\begin{array}{ccccc}4+1& 1+0& -1-1& 3+1& 4+0\\ 1-6& 2+8& -2+2& -1-3& 0-7\end{array}\right]\\ =\left[\begin{array}{ccccc}5& 1& -2& 4& 4\\ -5& 10& 0& -4& -7\end{array}\right]\end{array}$

(b)

To determine

To calculate:A-B

Answer to Problem 13E

  $\left[\begin{array}{ccccc}3& 1& 0& 2& 4\\ 7& -6& -4& 2& 7\end{array}\right]$

Explanation of Solution

Calculation:

To find $A-B$ , subtract corresponding elements of B from A

  $\begin{array}{l}A-B=\left[\begin{array}{ccccc}4& 1& -1& 3& 4\\ 1& 2& -2& -1& 0\end{array}\right]-\left[\begin{array}{ccccc}1& 0& -1& 1& 0\\ -6& 8& 2& -3& -7\end{array}\right]\\ =\left[\begin{array}{ccccc}4-1& 1-0& -1+1& 3-1& 4-0\\ 1+6& 2-8& -2-2& -1+3& 0+7\end{array}\right]\\ =\left[\begin{array}{ccccc}3& 1& 0& 2& 4\\ 7& -6& -4& 2& 7\end{array}\right]\end{array}$

(c)

To determine

To calculate: 3A

Answer to Problem 13E

  $\left[\begin{array}{ccccc}12& 3& -3& 9& 12\\ 3& 6& -6& -3& 0\end{array}\right]$

Explanation of Solution

Calculation:

To find 3A, multiply each element of matrix A by 3

  $3A=3\left[\begin{array}{ccccc}4& 1& -1& 3& 4\\ 1& 2& -2& -1& 0\end{array}\right]=\left[\begin{array}{ccccc}12& 3& -3& 9& 12\\ 3& 6& -6& -3& 0\end{array}\right]$

(d)

To determine

To calculate: $3A-2B$

Answer to Problem 13E

  $\left[\begin{array}{ccccc}10& 3& -1& 7& 12\\ 15& -10& -10& 3& 14\end{array}\right]$

Explanation of Solution

Calculation:

First find 3A

  $3A=3\left[\begin{array}{ccccc}4& 1& -1& 3& 4\\ 1& 2& -2& -1& 0\end{array}\right]=\left[\begin{array}{ccccc}12& 3& -3& 9& 12\\ 3& 6& -6& -3& 0\end{array}\right]$

Then find 2B

  $2B=2\left[\begin{array}{ccccc}1& 0& -1& 1& 0\\ -6& 8& 2& -3& -7\end{array}\right]=\left[\begin{array}{ccccc}2& 0& -2& 2& 0\\ -12& 16& 4& -6& -14\end{array}\right]$

Now find $3A-2B$

  $\begin{array}{l}3A-2B=\left[\begin{array}{ccccc}12& 3& -3& 9& 12\\ 3& 6& -6& -3& 0\end{array}\right]-\left[\begin{array}{ccccc}2& 0& -2& 2& 0\\ -12& 16& 4& -6& -14\end{array}\right]\\ =\left[\begin{array}{ccccc}10& 3& -1& 7& 12\\ 15& -10& -10& 3& 14\end{array}\right]\end{array}$