Chapter 10, Problem 50RE

To determine

To carry out: The indicated operation and explain if it is cannot be solved.

Answer to Problem 50RE

The dimension of matrix $5B$ is not equal to the dimension of matrix $2C$ .

So $5B-2C$ is not defined.

Explanation of Solution

Given:

  $B=\left[\begin{array}{ccc}1& 2& 4\\ -2& 1& 0\end{array}\right]$

  $C=\left[\begin{array}{cc}\frac{1}{2}& 3\\ 2& \frac{3}{2}\\ -2& 1\end{array}\right]$

  $5B-2C$

Calculation:

Consider the following matrices,

  $B=\left[\begin{array}{ccc}1& 2& 4\\ -2& 1& 0\end{array}\right]$

  $C=\left[\begin{array}{cc}\frac{1}{2}& 3\\ 2& \frac{3}{2}\\ -2& 1\end{array}\right]$

Thus,

  $5B=5\left[\begin{array}{ccc}1& 2& 4\\ -2& 1& 0\end{array}\right]$

  $=\left[\begin{array}{ccc}5& 10& 20\\ -10& 5& 0\end{array}\right]$

And

  $2C=2\left[\begin{array}{cc}\frac{1}{2}& 3\\ 2& \frac{3}{2}\\ -2& 1\end{array}\right]$

  $=\left[\begin{array}{cc}1& 6\\ 4& 3\\ -4& 2\end{array}\right]$

The dimension of the matrix $5B=\left[\begin{array}{ccc}5& 10& 20\\ -10& 5& 0\end{array}\right]$ is $2\times 3$ ( $2$ rows by $3$ columns) and the dimension of the matrix $2C=\left[\begin{array}{cc}1& 6\\ 4& 3\\ -4& 2\end{array}\right]$ is $3\times 2$ (3 rows by 2 columns)

Conclusion:

Thus the dimension of matrix $5B$ is not equal to the dimension of matrix $2C$ .So $5B-2C$ is not defined.