$ \left( \begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array} \right) % \left( \begin{array}{cc} a \\ b \end{array} \right) % = % \left( \begin{array}{cc} 3 - X \\ 6 - X \end{array} \right) $
Can anyone please verify if my answer is correct:
$a = 1-0.66X$
$b = 1+0.32X$
The matrix equation $\begin{bmatrix}1&2\\2&1\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}=\begin{bmatrix}3-X\\6-X\end{bmatrix}$
is equivalent to the system of equations:
$$\begin{cases}a+2b=3-X\\ 2a+b=6-X\end{cases}$$
Taking twice the second line and subtracting the first implies the equation: $2(2a+b)-(a+2b)=2(6-X)-(3-X)$, or simplified $3a = 9-X$. In other words, $a=3-\frac{1}{3}X$
Do so similarly for finding $b$.