Question

Let $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$ and $C=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$. Find the value of $3A-2B+3C$.

Answer 1

$A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],$ $B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$ and $C=\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$

$\Rightarrow$ $3A-2B+3C=3\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right]-2\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]+3\left[\begin{array}{cc}-2& 5\\ 3& 4\end{array}\right]$

$=\left[\begin{array}{cc}2\times 3& 4\times 3\\ 3\times 3& 2\times 3\end{array}\right]-\left[\begin{array}{cc}1\times 2& 3\times 2\\ -2\times 2& 5\times 2\end{array}\right]+\left[\begin{array}{cc}-2\times 3& 5\times 3\\ 3\times 3& 4\times 3\end{array}\right]$

$=\left[\begin{array}{cc}6& 12\\ 9& 6\end{array}\right]-\left[\begin{array}{cc}2& 6\\ -4& 10\end{array}\right]+\left[\begin{array}{cc}-6& 15\\ 9& 12\end{array}\right]$

$=\left[\begin{array}{cc}6-2& 12-6\\ 9-(-4)& 6-10\end{array}\right]+\left[\begin{array}{cc}-6& 15\\ 9& 12\end{array}\right]$

$=\left[\begin{array}{cc}4& 6\\ 13& -4\end{array}\right]+\left[\begin{array}{cc}-6& 15\\ 9& 12\end{array}\right]$

$=\left[\begin{array}{cc}4+(-6)& 6+15\\ 13+9& -4+12\end{array}\right]$

$=\left[\begin{array}{cc}-2& 21\\ 22& 8\end{array}\right]$