If [ * 20 c 2 + x &3&4 1& - 1 &2 &1& - 5 ]is a singular matrix, t… - Vidyadip

MCQ

If $\left[ {\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ - 1}&2\\x&1&{ - 5}\end{array}} \right]$is a singular matrix, then $x$ is

A
$\frac{{13}}{{25}}$
✓
$ - \frac{{25}}{{13}}$
C
$\frac{5}{{13}}$
D
$\frac{{25}}{{13}}$

✓

Answer

Correct option: B.

$ - \frac{{25}}{{13}}$

b
(b) Given, $\left| {\,\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ - 1}&2\\x&1&{ - 5}\end{array}\,} \right|\, = 0$

==> $(2 + x)(5 - 2) - 3( - 5 - 2x) + 4(1 + x) = 0$

==> $6 + 3x + 15 + 6x + 4 + 4x = 0$

==> $13x = - 25 \Rightarrow x = - \frac{{25}}{{13}}$.

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