Question

If $A+2B=$$\left|\begin{array}{cc}5& 5\\ 4& 0\end{array}\right|$ and $2A-B=\left|\begin{array}{cc}0& -5\\ 3& 5\end{array}\right|$, then A+B=

• A. $\left|\begin{array}{cc}3& 2\\ 3& 1\end{array}\right|$
• B. $\left|\begin{array}{cc}2& 3\\ 1& 3\end{array}\right|$
• C. $\left|\begin{array}{cc}2& 3\\ 1& -1\end{array}\right|$
• D. $\left|\begin{array}{cc}1& -1\\ 2& 1\end{array}\right|$

Answer 1

Answer: (A)

The correct option is A $\left|\begin{array}{cc}3& 2\\ 3& 1\end{array}\right|$
A+2B=$\left|\begin{array}{cc}5& 5\\ 4& 0\end{array}\right|$
Multiplying both sides by 2 we get
2A+4B=$\left|\begin{array}{cc}10& 10\\ 8& 0\end{array}\right|$....(1)
And 2A-B=$\left|\begin{array}{cc}0& -5\\ 3& 5\end{array}\right|$....(2)
Subtracting (2) from (1) we get
5B=$\left|\begin{array}{cc}10& 15\\ 5& -5\end{array}\right|$
$\therefore B=\left|\begin{array}{cc}2& 3\\ 1& -1\end{array}\right|$
From (1),
A=$\left|\begin{array}{cc}5& 5\\ 4& 0\end{array}\right|-\left|\begin{array}{cc}4& 6\\ 2& -2\end{array}\right|=\left|\begin{array}{cc}1& -1\\ 2& 2\end{array}\right|$
$\therefore A+B=\left|\begin{array}{cc}3& 2\\ 3& 1\end{array}\right|$