Assertion (A) : If [ ll x & 1 ] [ cc 1 & 0 -2 & 3 ] [ c x -5 ]=0,… - Vidyadip

Question

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

✓

Answer

Given $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$
$ \begin{array}{l} \Rightarrow [(x-2) 3]\left[\begin{array}{c} x \\ -5 \end{array}\right]\end{array}=0 $
$ \Rightarrow x(x-2)-15=0$
$ \Rightarrow x^2-2 x-15=0 $
$\Rightarrow x=-3,5$
$\therefore$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.

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