Question

If P =${\displaystyle \left|\begin{array}{cc}1& 2\\ 3& 4\end{array}\right|}$ , Q = ${\displaystyle \left|\begin{array}{cc}5& 1\\ 7& 4\end{array}\right|}$ and R = ${\displaystyle \left|\begin{array}{cc}2& 1\\ 4& 2\end{array}\right|}$   find the value of  (R + Q)P

Answer 1

R + Q = ${\displaystyle \left|\begin{array}{cc}2& 1\\ 4& 2\end{array}\right|+\left|\begin{array}{cc}5& 1\\ 7& 4\end{array}\right|}$

= ${\displaystyle {\left|\begin{array}{cc}7& 2\\ 11& 6\end{array}\right|}_{2\times 2}}$

 

(R + Q)P = ${\displaystyle \left|\begin{array}{cc}7& 2\\ 11& 6\end{array}\right| \left|\begin{array}{cc}1& 2\\ 3& 4\end{array}\right|}$

 

${\displaystyle =\left|\begin{array}{cc}7+6& 14+8\\ 11+18& 22+24\end{array}\right|}$

 

${\displaystyle ={\left|\begin{array}{cc}13& 22\\ 29& 46\end{array}\right|}_{2\times 2}}$