For what value(s) of k is A = \(\begin{bmatrix}k^2 & 4 \\4 & 2k \end{bmatrix}\) is not a singular matrix

\(\mathbb R- \{2\}\)

Firstly we start by determining the values where the matrix will be singular.

Finding the determinant and equating it to 0.

\(2 { k }^{ 3 } - 16 = 0\)

\(2 ({ k }^{ 3 } - 8) = 0\)

\({ k }^{ 3 } - 8= 0\)

\({ k }^{ 3 } = 8\)

k =2 

So excluding these values, the matrix will be non-singular for all real values of k