For what value(s) of k is A = \(\begin{bmatrix}3k^2 & 9 \\9 & k \end{bmatrix}\) is not a singular matrix
Answer & explanation
Correct answer: option 2
Firstly we start by determining the values where the matrix will be singular.
Finding the determinant and equating it to 0.
\(3 { k }^{ 3 } - 81 = 0\)
\(3 ({ k }^{ 3 } - 27) = 0\)
\({ k }^{ 3 } - 27= 0\)
\({ k }^{ 3 } = 27\)
k =3
So excluding these values, the matrix will be non-singular for all real values of k