Question

Find matrix $X$ such that $3A-2B+3I+X=0$ where $A=\left[\begin{array}{cc}4& 2\\ 1& 3\end{array}\right],B=\left[\begin{array}{cc}-2& 1\\ 3& 2\end{array}\right]$

Answer 1

$A=\left[\begin{array}{cc}4& 2\\ 1& 3\end{array}\right],B=\left[\begin{array}{cc}-2& 1\\ 3& 2\end{array}\right],I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Now,

$3A-2B+3I+X=0$

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

$\left[\begin{array}{cc}12& 6\\ 3& 9\end{array}\right]-\left[\begin{array}{cc}-4& 2\\ 6& 4\end{array}\right]+\left[\begin{array}{cc}3& 0\\ 0& 3\end{array}\right]+X=0$

$\left[\begin{array}{cc}12+4+3& 6-2+0\\ 3-6+0& 9-4+3\end{array}\right]+X=0$

$\left[\begin{array}{cc}19& 4\\ -3& 8\end{array}\right]+X=0$

$X=\left[\begin{array}{cc}-19& -4\\ 3& -8\end{array}\right]$