Chapter 3, Problem 4SGR

To determine

To fill the blank space: A matrix can be multiplied by a constant called a(n) …………….

Answer to Problem 4SGR

A matrix can be multiplied by a constant called a ……scalar……….

Explanation of Solution

Given information :

Given a matrix can be multiplied by a constant.

For example $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ be a $2\times 2$ matrix and it multiplied by a constant value $k$ then

  $\begin{array}{l}kA=k\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\\ \therefore kA=\left[\begin{array}{cc}k& 2k\\ 3k& 4k\end{array}\right]\end{array}$

Thus, $k$ is called a scalar.

A matrix can be multiplied by a constant called a scalar.