# How to solve for X. first row (8 ,-6) second row (-6,5) +4X= first row (-5,9) second row (4,4) ?

Sep 11, 2015

#### Explanation:

image of the question

Sep 12, 2015

Let $X = \left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$,

Then $4 X = \left(\begin{matrix}4 a & 4 b \\ 4 c & 4 d\end{matrix}\right)$,

In order to get:

$\left(\begin{matrix}8 & - 6 \\ - 6 & 5\end{matrix}\right) + 4 X = \left(\begin{matrix}- 5 & 9 \\ 4 & 4\end{matrix}\right)$

we need:

$8 + 4 a = - 5$, so $a = - \frac{13}{4}$

$- 6 + 4 b = 9$, so $b = \frac{15}{4}$

$- 6 + 4 c = 4$, so $c = \frac{5}{2}$

$5 + 4 d = 4$, so $d = - \frac{1}{4}$

Therefore,

$X = \left(\begin{matrix}- \frac{13}{4} & \frac{15}{4} \\ \frac{5}{2} & - \frac{1}{4}\end{matrix}\right)$