Chapter 7.5, Problem 20E

a.

To determine

To find: $A+B.$

Answer to Problem 20E

  $A+B$ can’t be determined.

Explanation of Solution

Given information:

  $A=\left[\begin{array}{c}3\\ 2\\ -1\end{array}\right]\text{and}B=\left[\begin{array}{ccc}-4& 6& 2\end{array}\right]$

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by $a\times b$ .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculations:

The order of matrix $A$ is $3\times 1$ and that of matrix $B$ is $1\times 3$ .

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 20E

  $A-B$ can’t be determined.

Explanation of Solution

Given information:

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by $a\times b$ .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculations:

The order of matrix $A$ is $3\times 1$ and that of matrix $B$ is $1\times 3$ .

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

c.

To determine

To find: $3A$

Answer to Problem 20E

The matrix $3A=\left[\begin{array}{c}9\\ 6\\ -3\end{array}\right]$

Explanation of Solution

Given information:

  $A=\left[\begin{array}{c}3\\ 2\\ -1\end{array}\right]\text{and}B=\left[\begin{array}{ccc}-4& 6& 2\end{array}\right]$

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by $a\times b$ .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculations:

  $\begin{array}{l}3A=3\left[\begin{array}{c}3\\ 2\\ -1\end{array}\right]\\ =\left[\begin{array}{c}3\times 3\\ 3\times 2\\ 3\times (-1)\end{array}\right]\\ =\left[\begin{array}{c}9\\ 6\\ -3\end{array}\right]\end{array}$

d.

To determine

To find: $3A-2B$

Answer to Problem 20E

  $3A-2B$ can’t be determined.

Explanation of Solution

Given information:

  $A=\left[\begin{array}{c}3\\ 2\\ -1\end{array}\right]\text{and}B=\left[\begin{array}{ccc}-4& 6& 2\end{array}\right]$

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by $a\times b$ .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculations:

  $\begin{array}{l}3A=3\left[\begin{array}{c}3\\ 2\\ -1\end{array}\right]\\ =\left[\begin{array}{c}3\times 3\\ 3\times 2\\ 3\times (-1)\end{array}\right]\\ =\left[\begin{array}{c}9\\ 6\\ -3\end{array}\right]\end{array}$

And

  $2B=2\left[\begin{array}{ccc}-4& 6& 2\end{array}\right]=\left[\begin{array}{ccc}2\times (-4)& 2\times 6& 2\times 2\end{array}\right]=\left[\begin{array}{ccc}-8& 12& 4\end{array}\right]$

The order of $3A$ is $3\times 1$ and that of $2B$ is $1\times 3$ . Since they are different, $3A-2B$ can’t be performed.