MCQ
Assertion : Let $A=\left[\begin{array}{ll}2 & 3 \\ 7 & 5\end{array}\right]$ and
$B =\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right]$ If $2 A= B$,
then $m=7$ and $n=3$.
Reason : Two equal matrices have the same order and their corresponding elements are also equal.
  • Both assertion and reason are correct and reason is the correct explanation of assertion.
  • B
    Both assertion and reason are correct but reason is not the correct explanation of assertion.
  • C
    Assertion is correct but reason is incorrect.
  • D
    Assertion is incorrect but reason is correct.

Answer

Correct option: A.
Both assertion and reason are correct and reason is the correct explanation of assertion.
(a) Both assertion and reason are correct and reason is the correct explanation of assertion.
Explanation:
$\begin{array}{l}2 A= B \\ \Rightarrow 2\left[\begin{array}{ll}2 & 3 \\ 7 & 5\end{array}\right]=\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right] \\ \Rightarrow\left[\begin{array}{cc}4 & 6 \\ 14 & 10\end{array}\right]=\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right] \\ \Rightarrow m-n=4 \text { and } m+n=10\end{array}$
Solving the two equations for $m$ and $n$, we get
$m=7$ and $n=3$.

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