Q71 / 180 · COMEDK 2016 · Mathematics
If $2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]$ and $A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right]$, then $B=$
- A$\left[\begin{array}{ccc}8 & 1 & 2 \\ 1 & 10 & 1\end{array}\right]$
- B$\left[\begin{array}{ccc}8 & 1 & -2 \\ -1 & 10 & -1\end{array}\right]$
- Correct answerC$\left[\begin{array}{ccc}8 & 1 & 2 \\ -1 & 10 & -1\end{array}\right]$
- D$\left[\begin{array}{ccc}8 & -1 & 2 \\ -1 & 10 & -1\end{array}\right]$
Solution
We have, $2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]...(i)$
and $A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right]...(ii)$
Multiply Eq. (ii) by 2 , we get
$2 A+4 B=\left[\begin{array}{ccc}
10 & 0 & 6 \\
2 & 12 & 4
\end{array}\right]...(iii)$
Now, subtracting Eq. (i) from Eq. (iii), we get
$B=\left[\begin{array}{ccc}
10 & 0 & 6 \\
2 & 12 & 4
\end{array}\right]-\left[\begin{array}{ccc}
2 & -1 & 4 \\
3 & 2 & 5
\end{array}\right]=\left[\begin{array}{ccc}
8 & 1 & 2 \\
-1 & 10 & -1
\end{array}\right]$
Hence, the correct answer is option: 'C'.