Question

If A is a matrix such that $\left(\begin{array}{cc}2& 1\\ 3& 2\end{array}\right)A\left(11\right)=\left(\begin{array}{cc}1& 1\\ 0& 0\end{array}\right)$ then A=

• A. $\left(\begin{array}{cc}1& 1\\ 0& 1\end{array}\right)$
• B. $(2,1)$
• C. $\left(\begin{array}{cc}1& 0\\ -1& 0\end{array}\right)$
• D. $\left(\begin{array}{c}2\\ -3\end{array}\right)$

Answer 1

The correct option is D

$\left(\begin{array}{c}2\\ -3\end{array}\right)$

$\text{Let}A={\left[\begin{array}{c}x\\ y\end{array}\right]}_{2\times 1}\Rightarrow \begin{array}{c}2x+y=1\\ 3x+2y=0\end{array}\Rightarrow x=2,y=-3$