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3 and 4 .Determinants and Matrices
easy
यदि $\left[ {\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ - 1}&2\\x&1&{ - 5}\end{array}} \right]$अव्युत्क्रमणीय आव्यूह हो, तो $x$ का मान होगा
A
$\frac{{13}}{{25}}$
B
$ - \frac{{25}}{{13}}$
C
$\frac{5}{{13}}$
D
$\frac{{25}}{{13}}$
Solution
(b)दिया है, $\left| {\,\begin{array}{*{20}{c}}{2 + x}&3&4\\1&{ – 1}&2\\x&1&{ – 5}\end{array}\,} \right|\, = 0$
==> $(2 + x)(5 – 2) – 3( – 5 – 2x) + 4(1 + x) = 0$
==> $6 + 3x + 15 + 6x + 4 + 4x = 0$
==> $13x = – 25 \Rightarrow x = – \frac{{25}}{{13}}$.
Standard 12
Mathematics