Chapter 7.5, Problem 26E

To determine

To evaluate: the given expression.

Answer to Problem 26E

  $\frac{4}{5}\left[\begin{array}{cc}14& -11\\ -22& 19\end{array}\right]+7\left[\begin{array}{cc}-22& 20\\ 13& 6\end{array}\right]=\left[\begin{array}{cc}-142.8& 131.2\\ 73.4& 57.2\end{array}\right]$

Explanation of Solution

Given:

Given expression

  $\frac{4}{5}\left[\begin{array}{cc}14& -11\\ -22& 19\end{array}\right]+7\left[\begin{array}{cc}-22& 20\\ 13& 6\end{array}\right]$

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.

Calculation:

Let us consider the following matrix expression

  $\frac{4}{5}\left[\begin{array}{cc}14& -11\\ -22& 19\end{array}\right]+7\left[\begin{array}{cc}-22& 20\\ 13& 6\end{array}\right]$

Use the matrix capabilities of a graphing utility to evaluate the expression and for that we feed the expression and get the result as

  $\begin{array}{c}>A:=matrix\left(\left[14,-11\right],\left[-22,19\right]\right)\\ \left[\begin{array}{cc}14& -11\\ -22& 19\end{array}\right]\\ B:=scalarmul\left(A,0.8\right)\\ \left[\begin{array}{cc}11.2& -8.8\\ -17.6& 15.2\end{array}\right]\\ C:=matrix\left(\left[\left[-22,20\right],\left[13,6\right]\right]\right)\\ \left[\begin{array}{cc}-22& 20\\ 13& 6\end{array}\right]\\ d:=scalarmul\left(C,7\right)\\ \left[\begin{array}{cc}-154& 140\\ 13& 6\end{array}\right]\\ E:=matadd\left(B,d\right)\\ \left[\begin{array}{cc}-142.8& 131.2\\ 73.4& 57.2\end{array}\right]\end{array}$