Chapter 8, Problem 39RE

a.

To determine

Sum of matrix A+B

Answer to Problem 39RE

Sum of matrix is;

  $\left[\begin{array}{l}\text{5 7}\\ \text{-3 14}\\ \text{31 42}\end{array}\right]$

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right],B=\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]$

Dimension of matrix A is $3\times 2$ and size of matrix B is $3\times 2$ both matrix are of same order therefore sum of the matrix is possible.

And size of matrix A+B will be $3\times 2$

Therefore. sum of matrix,

  $\begin{array}{l}A+B=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right]+\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]\\ =\left[\begin{array}{l}\text{5 7}\\ \text{-3 14}\\ \text{31 42}\end{array}\right]\end{array}$

b.

To determine

Subtraction of matrix $A-B$

Answer to Problem 39RE

Subtraction of matrix is;

  $\left[\begin{array}{l}\text{5 1}\\ \text{-11 -10}\\ \text{-9 -38}\end{array}\right]$

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right],B=\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]$

Dimension of matrix A is $3\times 2$ and size of matrix B is $3\times 2$ so order of both matrix are same therefore subtraction of the matrix is possible.

And size of matrix A-B will be $3\times 2$

Therefore. subtraction of matrix,

  $\begin{array}{l}A-B=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right]-\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]\\ =\left[\begin{array}{l}\text{5 1}\\ \text{-11 -10}\\ \text{-9 -38}\end{array}\right]\end{array}$

c.

To determine

Expression of matrix 4A

Answer to Problem 39RE

Matrix 4A is;

  $\left[\begin{array}{l}\text{20 16}\\ \text{-28 8}\\ \text{44 8}\end{array}\right]$

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right],B=\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]$

  $\begin{array}{l}4A=4\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right]\\ =\left[\begin{array}{l}\text{20 16}\\ \text{-28 8}\\ \text{44 8}\end{array}\right]\end{array}$

d.

To determine

Expression of matrix A+3B

Answer to Problem 39RE

Matrix A+3B is;

  $\left[\begin{array}{l}\text{5 13}\\ \text{5 38}\\ \text{71 162}\end{array}\right]$

Explanation of Solution

Given:

Matrices are given as;

  $A=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right],B=\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]$

  $\begin{array}{l}A+3B=\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right]+3\left[\begin{array}{l}\text{0 3}\\ \text{4 12}\\ \text{20 40}\end{array}\right]\\ =\left[\begin{array}{l}\text{5 4}\\ \text{-7 2}\\ \text{11 2}\end{array}\right]+\left[\begin{array}{l}\text{0 9}\\ \text{12 36}\\ \text{60 120}\end{array}\right]\\ =\left[\begin{array}{l}\text{5 13}\\ \text{5 38}\\ \text{71 162}\end{array}\right]\end{array}$