The matrix A satisfying A [ ll 1 & 5 0 & 1 ]= [ cc 3 & -1 6 & 0 ]… - Vidyadip

MCQ

The matrix A satisfying $A \left[\begin{array}{ll}1 & 5 \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}3 & -1 \\ 6 & 0\end{array}\right]$ is

A
$\left[\begin{array}{cc}3 & 2 \\ 6 & -3\end{array}\right]$
✓
$\left[\begin{array}{ll}3 & -16 \\ 6 & -30\end{array}\right]$
C
$\left[\begin{array}{cc}3 & -16 \\ 6 & 30\end{array}\right]$
D
$\left[\begin{array}{cc}3 & -3 \\ 6 & 2\end{array}\right]$

✓

Answer

Correct option: B.

$\left[\begin{array}{ll}3 & -16 \\ 6 & -30\end{array}\right]$

(B) If $AC = B$, then $A = BC ^{-1}$
$\therefore \quad A=\left[\begin{array}{cc}3 & -1 \\ 6 & 0\end{array}\right]\left[\begin{array}{cc}1 & 5 \\ 0 & 1\end{array}\right]^{-1}$
$=\left[\begin{array}{cc}3 & -1 \\ 6 & 0\end{array}\right]\left[\begin{array}{cc}1 & -5 \\ 0 & 1\end{array}\right]$
$=\left[\begin{array}{ll}3 & -16 \\ 6 & -30\end{array}\right]$

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