Matrix A = [ * 20 c 1&0& - k 2&1&3 &0&1 ] is invertible for - Vidyadip

MCQ

Matrix $A = \left[ {\begin{array}{*{20}{c}}1&0&{ - k}\\2&1&3\\k&0&1\end{array}} \right]$ is invertible for

A
$k = 1$
B
$k = - 1$
C
$k = 0$
✓
All real $k$

✓

Answer

Correct option: D.

All real $k$

d
(d) On expansion, $|A| = {k^2} + 1$, which can be never zero.

.Hence matrix $A$ is invertible for all real $k.$

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