The matrix ( * 20 c 1&a&2 1&2&5 2&1&1 ) is not invertible, if ‘a’… - Vidyadip

MCQ

The matrix $\left( {\begin{array}{*{20}{c}}1&a&2\\1&2&5\\2&1&1\end{array}} \right)$ is not invertible, if $‘a’ $ has the value

A
$2$
✓
$1$
C
$0$
D
$-1$

✓

Answer

Correct option: B.

$1$

b
(b) The matrix is not invertible if $\left| {\,\begin{array}{*{20}{c}}1&a&2\\1&2&5\\2&1&1\end{array}\,} \right| = 0$

$ \Rightarrow $ $1\,(2 - 5) - a(1 - 10) + 2(1 - 4) = 0$

$ \Rightarrow $ $ - 3 + 9a - 6 = 0 $

$\Rightarrow a = 1$.

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