Find the matrix X such that
Question:

Find the matrix X such that 2A – B + X = O,

where $\mathrm{A}=\left[\begin{array}{ll}3 & 1 \\ 0 & 2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]$

Solution:

Given 2A – B + X = 0

$2\left(\left[\begin{array}{ll}3 & 1 \\ 0 & 2\end{array}\right]\right)-\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]+X=0$

$X=\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]-2\left(\left[\begin{array}{ll}3 & 1 \\ 0 & 2\end{array}\right]\right)$

$=\left[\begin{array}{cc}-2 & 1 \\ 0 & 3\end{array}\right]-\left[\begin{array}{ll}6 & 2 \\ 0 & 4\end{array}\right]$

$=\left[\begin{array}{cc}-8 & -1 \\ 0 & -1\end{array}\right]$

Conclusion: $X=\left[\begin{array}{cc}-8 & -1 \\ 0 & -1\end{array}\right]$