If B= [ ll 1 & 5 0 & 3 ] and A-2 B= [ cc 0 & 4 -7 & 5 ] then the … - Vidyadip

MCQ

If $B=\left[\begin{array}{ll}1 & 5 \\ 0 & 3\end{array}\right]$ and $A-2 B=\left[\begin{array}{cc}0 & 4 \\ -7 & 5\end{array}\right]$ then the matrix $A$ is equal to

A
$\left[\begin{array}{cc}2 & 14 \\ -7 & 11\end{array}\right]$
B
$\left[\begin{array}{cc}-2 & 14 \\ 7 & 11\end{array}\right]$
C
$\left[\begin{array}{cc}2 & -14 \\ 7 & 11\end{array}\right]$
✓
$\left[\begin{array}{ll}-2 & 14 \\ -7 & 11\end{array}\right]$

✓

Answer

Correct option: D.

$\left[\begin{array}{ll}-2 & 14 \\ -7 & 11\end{array}\right]$

$
B=\left[\begin{array}{ll}
1 & 5 \\
0 & 3
\end{array}\right]
$
and
$
\begin{aligned}
& A -2 B =\left[\begin{array}{cc}
0 & 4 \\
-7 & 5
\end{array}\right] \\
& 2 B =2 \times\left[\begin{array}{cc}
-1 & 5 \\
0 & 3
\end{array}\right]=\left[\begin{array}{cc}
-2 & 10 \\
0 & 6
\end{array}\right] \\
& A -2 B =\left[\begin{array}{cc}
0 & 4 \\
-7 & 5
\end{array}\right] \\
& \Rightarrow A =\left[\begin{array}{cc}
0 & 4 \\
-7 & 5
\end{array}\right]+2 B \\
& \Rightarrow A =\left[\begin{array}{cc}
0 & 4 \\
-7 & 5
\end{array}\right]+\left[\begin{array}{cc}
2 & 10 \\
0 & 6
\end{array}\right] \\
& =\left[\begin{array}{cc}
0-2 & 4+10 \\
-7+0 & 5+6
\end{array}\right] \\
& =\left[\begin{array}{cc}
-2 & 14 \\
-7 & 11
\end{array}\right] .
\end{aligned}
$

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