The determinant of a certain matrix depends on a real parameter and is given by

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The determinant of a certain

3\times3

matrix depends on a real parameter

k

and is given by

D(k)=4(k-1)^2

. Answer the following: (i) State the value(s) of

k

for which the matrix is singular. (ii) How many distinct real values of

k

make the matrix invertible?