Question

Solve for X. Assume X is a 2 x 2 matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated. [9 9 - 9 -9] x + [6 3 7 9] = [-1 8 -4 6] x.

Answer 1

Answer:

$X=\left[\begin{array}{cc}-\frac{97}{145}&-\frac{54}{145}\\\\\frac{20}{29}&\frac{21}{29}\end{array}\right]$

Step-by-step explanation:

$\left[\begin{array}{cc}9&9\\-9&-9\end{array}\right] X+\left[\begin{array}{cc}6&3\\7&9\end{array}\right] =\left[\begin{array}{cc}-1&8\\-4&6\end{array}\right] X$

$Assume\:\:\:X=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

$9a+9c+6=-a+8c\\-9a-9c+7=-4a+6c\\9b+9d+3=-b+8d\\-9b-9d+9=-4b+6d$

$10a+c=-6\\5a+15c=7$

$a=-\frac{97}{145} ,\:\:c=\frac{20}{29}$

$10b+d=-3\\5b+15d=9$

$b=-\frac{54}{145} ,\:\:d=\frac{21}{29}$

Hence,

$X=\left[\begin{array}{cc}-\frac{97}{145}&-\frac{54}{145}\\\\\frac{20}{29}&\frac{21}{29}\end{array}\right]$