It is given that X [ cc 3 & 2 1 & -1 ]= [ ll 4 & 1 2 & 3 ]. Then matrix X is :

It is given that X [ cc 3 & 2 1 & -1 ]= [ ll 4 & 1 2 & 3 ]. Then …

MCQ

It is given that $X\left[\begin{array}{cc}3 & 2 \\ 1 & -1\end{array}\right]=\left[\begin{array}{ll}4 & 1 \\ 2 & 3\end{array}\right]$. Then matrix $X$ is :

A
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
B
$\left[\begin{array}{cc}0 & -1 \\ 1 & 1\end{array}\right]$
C
$\left[\begin{array}{cc}1 & 1 \\ 1 & -1\end{array}\right]$
D
$\left[\begin{array}{ll}1 & -1 \\ 1 & -1\end{array}\right] \quad$

✓

Answer

Let $X=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$
We have, $x\left[\begin{array}{cc}3 & 2 \\ 1 & -1\end{array}\right]=\left[\begin{array}{ll}4 & 1 \\ 2 & 3\end{array}\right]$
$
\begin{array}{l}
\Rightarrow\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]\left[\begin{array}{cc}
3 & 2 \\
1 & -1
\end{array}\right]=\left[\begin{array}{ll}
4 & 1 \\
2 & 3
\end{array}\right] \\
\Rightarrow\left[\begin{array}{ll}
3 a+b & 2 a-b \\
3 c+d & 2 c-d
\end{array}\right]=\left[\begin{array}{ll}
4 & 1 \\
2 & 3
\end{array}\right]
\end{array}
$
On comparing the element of matrices, we get
$
\begin{array}{l}
3 a+b=4 \\
2 a-b=1 \\
3 c+d=2 \\
2 c-d=3
\end{array}
$
Adding (i) and (ii), we get $5 a=5 \Rightarrow a=1$
Putting $a=1$ in (i), we get $3(1)+b=4 \Rightarrow b=1$
Adding (iii) and (iv), we get $5 c=5 \Rightarrow c=1$
Putting $c=1$ in (iii), we get $3+d=2 \Rightarrow d=-1$
$
\therefore X=\left[\begin{array}{cc}
1 & 1 \\
1 & -1
\end{array}\right]
$

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