Question

$\left[\begin{array}{cc}3& 2\\ -1& -2\\ 4& 5\end{array}\right]\left[\begin{array}{cc}0& a\\ b& c\end{array}\right]=\left[\begin{array}{cc}-4& 9\\ 4& -7\\ -10& 19\end{array}\right]$
Find $a,b$ and $c$.

• A. $2,-1,3$
• B. $1,-2,3$
• C. $3,-2,1$
• D. $1,2,3$

Answer 1

Answer: (B)

$1,-2,3$

The product is $\left[\begin{array}{cc}3& 2\\ -1& -2\\ 4& 5\end{array}\right]\left[\begin{array}{cc}0& a\\ b& c\end{array}\right]=$ $\left[\begin{array}{cc}2b& 3a+2c\\ -2b& -2c-a\\ 5b& 5c+4a\end{array}\right]$

By given, we have

$\left[\begin{array}{cc}2b& 3a+2c\\ -2b& -2c-a\\ 5b& 5c+4a\end{array}\right]$ $=\left[\begin{array}{cc}-4& 9\\ 4& -7\\ -10& 19\end{array}\right]$

By comparing, we get

$b=-2,a=1,c=3$