Solve the matrix equation [(2,1)(5,0)] -3X = [(-7,4)(2,6)]

Question

Solve the matrix equation \(\begin{bmatrix}2&1\\[0.3em]5&0\end{bmatrix}\) -3X = \(\begin{bmatrix}-7&4\\[0.3em]2&6\end{bmatrix}\)

(a) X = \(\begin{bmatrix}3&1\\[0.3em]-1&2\end{bmatrix}\)

(b) X = \(\begin{bmatrix}3&-1\\[0.3em]1&-2\end{bmatrix}\)

(c) X = \(\begin{bmatrix}3&-1\\[0.3em]-1&-2\end{bmatrix}\)

(d) X = \(\begin{bmatrix}-3&-1\\[0.3em]1&-2\end{bmatrix}\)

Answer 1

(b)   \(\begin{bmatrix}2&1\\[0.3em]5&0\end{bmatrix}\) -3X = \(\begin{bmatrix}-7&4\\[0.3em]2&6\end{bmatrix}\)

⇒ - 3X = \(\begin{bmatrix}-7&4\\[0.3em]2&6\end{bmatrix}\) - \(\begin{bmatrix}2&1\\[0.3em]5&0\end{bmatrix}\)

= \(\begin{bmatrix}-7-2&4-1\\[0.3em]2-5&6-0\end{bmatrix}\) = \(\begin{bmatrix}-9&3\\[0.3em]-3&6\end{bmatrix}\)

⇒ X = \(-\frac13\)\(\begin{bmatrix}-9&3\\[0.3em]-3&6\end{bmatrix}\) = \(\begin{bmatrix}\frac{-9}{-3}&\frac3{-3}\\[0.3em]\frac{-3}{-3}&\frac6{-3}\end{bmatrix}\) = \(\begin{bmatrix}3&-1\\[0.3em]1&-2\end{bmatrix}\)