Chapter 8, Problem 44RE

a.

To determine

Find theaddition of the given matrices.

Answer to Problem 44RE

There is no solution.

Explanation of Solution

Given information:

The givenmatricesare

  $A=\left[\begin{array}{ccc}6& -5& 7\end{array}\right]$ , $B=\left[\begin{array}{c}-1\\ 4\\ 8\end{array}\right]$

Calculation:

If $A=\left[a_{ij}\right]$ and $B=\left[b_{ij}\right]$ are matrices of order $m\times n$ , then their sum is the $m\times n$ matrix given by

  $A+B=\left[a_{ij}+b_{ij}\right]$

The sum of two matrices of different orders is undefined.

Now

The given matrices $A$ and $B$ a different order. The sum of two matrices of different orders is undefined.

Hence there is no solution.

b.

To determine

Find the subtraction of the given matrices.

Answer to Problem 44RE

Thereis no solution.

Explanation of Solution

Given information:

The given matrices are

  $A=\left[\begin{array}{ccc}6& -5& 7\end{array}\right]$ , $B=\left[\begin{array}{c}-1\\ 4\\ 8\end{array}\right]$

Calculation:

If $A=\left[a_{ij}\right]$ and $B=\left[b_{ij}\right]$ are matrices of order $m\times n$ , then their difference is the $m\times n$ matrix given by

  $A-B=\left[a_{ij}-b_{ij}\right]$

The difference of two matrices of different orders is undefined.

Now

The given matrices $A$ and $B$ have a different order. The difference of two matrices of different orders is undefined.

Hence there is no solution.

c.

To determine

Find the scalar multiplication of the given matrix.

Answer to Problem 44RE

The scalar multiplication of the matrix is $\left[\begin{array}{ccc}24& 20& 28\end{array}\right]$ .

Explanation of Solution

Given information:

The given matrixis

  $A=\left[\begin{array}{ccc}6& -5& 7\end{array}\right]$

and the scalar quantity is $4$ .

Calculation:

If $A=\left[a_{ij}\right]$ is an $m\times n$ matrix and $c$ is a scalar, then the scalar multiple of $A$ by $c$ is the $m\times n$ matrix given by

  $cA=\left[c{a}_{ij}\right]$

Now

  $\begin{array}{l}4A\\ =4\left[\begin{array}{ccc}6& -5& 7\end{array}\right]\\ =\left[\begin{array}{ccc}6\cdot 4& -5\cdot 4& 7\cdot 4\end{array}\right]\\ =\left[\begin{array}{ccc}24& 20& 28\end{array}\right]\end{array}$

Hence the scalar multiplication of the matrixis $\left[\begin{array}{ccc}24& 20& 28\end{array}\right]$ .

d.

To determine

Find the addition of matrices with scalar multiplication.

Answer to Problem 44RE

Thereis no solution.

Explanation of Solution

Given information:

The given matrices are

  $A=\left[\begin{array}{ccc}6& -5& 7\end{array}\right]$ , $B=\left[\begin{array}{c}-1\\ 4\\ 8\end{array}\right]$

and the given expression is $A+3B$ .

Calculation:

If $A=\left[a_{ij}\right]$ is an $m\times n$ matrix and $c$ is a scalar, then the scalar multiple of $A$ by $c$ is the $m\times n$ matrix given by

  $cA=\left[c{a}_{ij}\right]$

If $A=\left[a_{ij}\right]$ and $B=\left[b_{ij}\right]$ are matrices of order $m\times n$ , then their sum is the $m\times n$ matrix given by

  $A+B=\left[a_{ij}+b_{ij}\right]$

The sum of two matrices of different orders is undefined.

Now

  $\begin{array}{l}3B\\ =3\left[\begin{array}{c}-1\\ 4\\ 8\end{array}\right]\\ =\left[\begin{array}{c}-1\cdot 3\\ 4\cdot 3\\ 8\cdot 3\end{array}\right]\\ =\left[\begin{array}{c}-3\\ 12\\ 24\end{array}\right]\end{array}$

  $\begin{array}{l}A+3B\\ =A=\left[\begin{array}{ccc}6& -5& 7\end{array}\right]+\left[\begin{array}{c}-3\\ 12\\ 24\end{array}\right]\end{array}$

The given matrices $A$ and $B$ have a different order. The sum of two matrices of different orders is undefined.

Hence there is no solution.