For what value(s) of k is A = \(\begin{bmatrix}k^2 & 4 \\4 & 2k \end{bmatrix}\) is not a singular matrix
Answer & explanation
Correct answer: option 1
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