Question

If $A^{\prime }=\left[\begin{array}{cc}-2& 3\\ 1& 2\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& 0\\ 1& 2\end{array}\right]$, find ${\left[\begin{array}{c}A+2B\end{array}\right]}^{\prime }$.

Answer 1

Given,

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

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

Now, $A+2B=\left[\begin{array}{cc}-2& 1\\ 3& 2\end{array}\right]+\left[\begin{array}{cc}-2& 0\\ 2& 4\end{array}\right]=\left[\begin{array}{cc}-4& 1\\ 5& 6\end{array}\right]$

Therefore, ${\left[\begin{array}{c}A+2B\end{array}\right]}^{\prime }=\left[\begin{array}{cc}-4& 5\\ 1& 6\end{array}\right]$