Question

$\text{If}A=\left[\begin{array}{cc}2& 5\\ -3& 1\end{array}\right],B=\left[\begin{array}{cc}-2& 3\\ 7& 2\end{array}\right],\text{and}$

$C=\left[\begin{array}{cc}3& 5\\ -1& -2\end{array}\right],\text{find}AB+C.$


[2 marks]

• A. $\left[\begin{array}{cc}31& 16\\ 13& 7\end{array}\right]$
• B. $\left[\begin{array}{cc}34& 21\\ 12& -9\end{array}\right]$
• C. $\left[\begin{array}{cc}34& 21\\ 12& -5\end{array}\right]$
• D. $\left[\begin{array}{cc}31& 16\\ 13& 11\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}34& 21\\ 12& -9\end{array}\right]$

$AB=\left[\begin{array}{cc}2& 5\\ -3& 1\end{array}\right]\left[\begin{array}{cc}-2& 3\\ 7& 2\end{array}\right]=\left[\begin{array}{cc}2\times (-2)+5\times 7& 2\times 3+5\times 2\\ -3\times (-2)+1\times 7& -3\times 3+1\times 2\end{array}\right]=\left[\begin{array}{cc}31& 16\\ 13& -7\end{array}\right]AB+C=\left[\begin{array}{cc}31& 16\\ 13& -7\end{array}\right]+\left[\begin{array}{cc}3& 5\\ -1& -2\end{array}\right]=\left[\begin{array}{cc}34& 21\\ 12& -9\end{array}\right]$