Question

If the matrix $\left[\begin{array}{ccc}-1& 3& 2\\ 1& k& -3\\ 1& 4& 5\end{array}\right]$ has an inverse then the values of $k$.

• A. $k$ is any real number
• B. $k=-4$
• C. $k\ne -4$
• D. $k\ne 4$

Answer 1

The correct option is C $k\ne -4$

For a matrix to be invertible, its determinant must not be zero.

$\therefore -1(5k+12)-3(5-(-3\left)\right)+2(4-k)\ne 0$

$\therefore -5k-12-24+8-2k\ne 0$

$\therefore -7k\ne 28$

$\therefore k\ne -4$