For the parameter

MATHEMATICS · Multi-part · CBSE · Mathematics · Determinants · Determinants

Problem

For the parameter

k \in \mathbb{R}

, consider the matrix

M(k)=\begin{pmatrix}k & 1 & 1\\ 1 & k & 1\\ 1 & 1 & k\end{pmatrix}.

Answer the following: (i) Evaluate

|M(k)|

in terms of

k

. (ii) Hence find all real values of

k

for which

M(k)

is singular. (iii) For

k = 2

, calculate

|M(2)|

and state whether an inverse of

M(2)

exists.