MCQ
If $A=\left[\begin{array}{ll}7 & 3 \\ 5 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 5 \\ 4 & 5\end{array}\right]$, then the matrix $C$ such that $2 A+3 C=8 B$, is:
  • A
    $\left[\begin{array}{cc}2 & 24 \\ 22 & 36\end{array}\right]$
  • $\left[\begin{array}{cc}\frac{2}{3} & \frac{34}{3} \\ \frac{22}{3} & \frac{36}{3}\end{array}\right]$
  • C
    $\left[\begin{array}{cc}\frac{2}{3} & \frac{22}{3} \\ \frac{36}{3} & \frac{34}{3}\end{array}\right]$
  • D
    $\left[\begin{array}{cc}1 & 17 \\ 11 & 18\end{array}\right]$

Answer

Correct option: B.
$\left[\begin{array}{cc}\frac{2}{3} & \frac{34}{3} \\ \frac{22}{3} & \frac{36}{3}\end{array}\right]$
(b) $\left[\begin{array}{cc}\frac{2}{3} & \frac{34}{3} \\ \frac{22}{3} & \frac{36}{3}\end{array}\right]$
Explanation:
We have,
$2 A+3 C=8 B$
$\begin{array}{l}\Rightarrow 3 C =8 B-2 A \\ =8\left[\begin{array}{ll}2 & 5 \\ 4 & 5\end{array}\right]-2\left[\begin{array}{ll}7 & 3 \\ 5 & 2\end{array}\right] \\ =\left[\begin{array}{ll}16 & 40 \\ 32 & 40\end{array}\right]-\left[\begin{array}{ll}14 & 6 \\ 10 & 4\end{array}\right] \\ =\left[\begin{array}{cc}2 & 34 \\ 22 & 36\end{array}\right] \\ \Rightarrow C=\frac{1}{3}\left[\begin{array}{cc}2 & 34\end{array}\right] \\ =\left[\begin{array}{cc}\frac{2}{3} & \frac{34}{3} \\ \frac{22}{3} & \frac{36}{3}\end{array}\right]\end{array}$

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