Chapter 6.5, Problem 50E

To determine

To find: matrix X .

Answer to Problem 50E

  $\left[\begin{array}{cc}\begin{array}{l}0\\ 0\end{array}& \begin{array}{l}0\\ 0\end{array}\end{array}\right]$

Explanation of Solution

Given information:

The given matrices are as follows:

  $X=\left[\begin{array}{cc}\begin{array}{l}1\\ 1\end{array}& \begin{array}{l}1\\ 1\end{array}\end{array}\right]\left[\begin{array}{cc}\begin{array}{l}3\\ -3\end{array}& \begin{array}{l}5\\ -5\end{array}\end{array}\right]$

Calculation:

Multiply the matrices on the right side as follows:

  $\begin{array}{c}X=\left[\begin{array}{cc}\begin{array}{l}1\\ 1\end{array}& \begin{array}{l}1\\ 1\end{array}\end{array}\right]\left[\begin{array}{cc}\begin{array}{l}3\\ -3\end{array}& \begin{array}{l}5\\ -5\end{array}\end{array}\right]\\ =\left[\begin{array}{cc}\begin{array}{l}\left(1\times 3\right)+\left(1\times \left(-3\right)\right)\\ \left(1\times 3\right)+\left(1\times \left(-3\right)\right)\end{array}& \begin{array}{l}\left(1\times 5\right)+\left(1\times \left(-5\right)\right)\\ \left(1\times 5\right)+\left(1\times \left(-5\right)\right)\end{array}\end{array}\right]\\ =\left[\begin{array}{cc}\begin{array}{l}3-3\\ 3-3\end{array}& \begin{array}{l}5-5\\ 5-5\end{array}\end{array}\right]\\ =\left[\begin{array}{cc}\begin{array}{l}0\\ 0\end{array}& \begin{array}{l}0\\ 0\end{array}\end{array}\right]\end{array}$

Thus matrix X is $\left[\begin{array}{cc}\begin{array}{l}0\\ 0\end{array}& \begin{array}{l}0\\ 0\end{array}\end{array}\right]$ .