If $A$ is a matrix such that $\left[\begin{array}{ll} 2 & 1 \ 3 & 2 \end{array} ight] A\left[\begin{array}{ll} 1 & 1 \end{array} ight]=\left[\begin{array}{ll} 1 & 1 \ 0 & 0 \end{array} ight]$ then $A$ is equal to

Question

If $A$ is a matrix such that $\left[\begin{array}{ll} 2 & 1 \ 3 & 2 \end{array}ight] A\left[\begin{array}{ll} 1 & 1 \end{array}ight]=\left[\begin{array}{ll} 1 & 1 \ 0 & 0 \end{array}ight]$ then $A$ is equal to

Aicharya · Accepted Answer

Let $\begin{aligned} & A=\left[\begin{array}{l}x_1 \ x_2\end{array}ight] \ & 	herefore \quad\left[\begin{array}{ll}2 & 1 \ 3 & 2\end{array}ight]\left[\begin{array}{l}x_1 \ x_2\end{array}ight]\left[\begin{array}{ll}1 & 1\end{array}ight] \ &=\left[\begin{array}{c}2 x_1+x_2 \ 3 x_1+2 x_2\end{array}ight]\left[\begin{array}{ll}1 & 1\end{array}ight] \ &=\left[\begin{array}{cc}2 x_1+x_2 & 2 x_1+x_2 \ 3 x_1+2 x_2 & 3 x_1+2 x_2\end{array}ight]\end{aligned}$ $\begin{aligned} & 	herefore \quad\left[\begin{array}{cc} 2 x_1+x_2 & 2 x_1+x_2 \ 3 x_1+2 x_2 & 3 x_1+2 x_2 \end{array}ight]=\left[\begin{array}{ll} 1 & 1 \ 0 & 0 \end{array}ight] \ & \Rightarrow 2 x_1+x_2=1 	ext { and } 3 x_1+2 x_2=0 \end{aligned}$ On solving, we get $\begin{aligned} & & x_1=2 \ and & & x_2=-3 \ & & A=\left[\begin{array}{r} 2 \ -3 \end{array}ight] \end{aligned}$

If $A$ is a matrix such that $\left[\begin{array}{ll} 2 & 1 \\ 3 & 2 \end{array}\right]…

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