Chapter 16, Problem 1RE

To determine

Find whether the matrix operation $2\left[\begin{array}{cc}3& -1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}6& -2\\ 0& 2\end{array}\right]$ is true or false.

Answer to Problem 1RE

The matrix operation $2\left[\begin{array}{cc}3& -1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}6& -2\\ 0& 2\end{array}\right]$ is False.

Explanation of Solution

Check the matrix operation as follows:

$\begin{array}{l}2\left[\begin{array}{cc}3& -1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}6& -2\\ 0& 2\end{array}\right]\\ \left[\begin{array}{cc}6& -2\\ 0& 4\end{array}\right]\ne \left[\begin{array}{cc}6& -2\\ 0& 2\end{array}\right]\\ \text{LHS}\ne \text{RHS}\end{array}$

Hence, $2\left[\begin{array}{cc}3& -1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}6& -2\\ 0& 2\end{array}\right]$ is not satisfied.

Therefore, the given matrix operation is false.

Thus, the matrix operation $2\left[\begin{array}{cc}3& -1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}6& -2\\ 0& 2\end{array}\right]$ is False.