NIMCET 2014 Question Paper with solutions

If given matrix A = $\left[\begin{array}{ccc}-1& 3& 2\\ 1& \mathit{k}& -3\\ 1& 4& 5\end{array}\right]$ is invertible, then | A | ≠ 0.
∴ |A| = - 1 (5k + 12) - 3 (3 + 5) + 2 (k - 4)
= - 5k - 12 - 24 + 8 - 2k
= - 28 - 7k
|A| ≠ 0
∴ 7k ≠ - 28
⇒ k ≠ - 4