Question

What is the solution of the matrix equation?

Answer 1

(-12, 2)

Explanation:

`\left[\begin{array}{ccc}1&1\\2&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}8\\36\end{array}\right] \\\\\left[\begin{array}{ccc}x+y\\2x+3y\end{array}\right] =\left[\begin{array}{ccc}8\\36\end{array}\right]\\.\qquad\qquad\Downarrow\\\left\{\begin{array}{ccc}x+y=8&|\text{multiply both sides by (-2)}\\2x+3y=36\end{array}\right`

`\underline{+\left\{\begin{array}{ccc}-2x-2y=-16\\2x+3y=36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad y=20\\\\\text{Put the value of y to the firast equation:}\\\\x+20=8\qquad\text{subtract 20 from both sides}\\x=-12\\\\\boxed{(-12,\ 20)}`