Question

Assertion :If $\left[x1\right]\left[\begin{array}{cc}1& 0\\ -2& 3\end{array}\right]\left[\begin{array}{c}x\\ -5\end{array}\right]=0$, then value of $x$ is either $-3$ or $5.$ Reason: Two matrices $\left[\begin{array}{cc}x& y\\ u& v\end{array}\right]$ & $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ are equal if & only if their corresponding entries are equal.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A),
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R} is false,
• D. (A)is false but (R} is true.

Answer 1

The correct option is B Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

Given $\left[x1\right]\left[\begin{array}{cc}1& 0\\ -2& 3\end{array}\right]\left[\begin{array}{c}x\\ -5\end{array}\right]=0$
$\Rightarrow \left[\begin{array}{cc}x-2& 3\end{array}\right]\left[\begin{array}{c}x\\ -5\end{array}\right]=0$
$\Rightarrow x(x-2)-15=0$
$\Rightarrow x^2-2x-15=0$
$\Rightarrow x=-3,5$
$\therefore$ Assertion (A) is correct.
We know that if two matrices are equal then their corresponding elements are also equal.
Hence, assertion (A) & reason (R) both are true but reason (R) is not the correct explanation of assertion (A).