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  4. Matrix A = [1&0&k 2&1&3 k&0&1] is not invertible for :

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Q. Matrix $A = \begin{bmatrix}1&0&k\\ 2&1&3\\ k&0&1\end{bmatrix} $ is not invertible for :

Matrices

Solution:

Let $A = \begin{bmatrix}1&0&k\\ 2&1&3\\ k&0&1\end{bmatrix} $
$ | A | = 1 (1 - 0) - 0 + k (0 - k) = 1 - k^2$
As we know matrix A will not be invertible if | A | = 0
$\therefore \ |A| = 0 \ \Rightarrow \ 1 - k^2 = 0$
$ \Rightarrow \ k^2 = 1 \ \Rightarrow \ k = \pm 1$
For, $k = \pm 1, | A | = 0 $