Let be a real parameter and let B(k)= pmatrix k &1 &2 2 &k &1 1 &2 &k pmatrix

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Let

k

be a real parameter and let

B(k)=\begin{pmatrix} k &1 &2\\ 2 &k &1\\ 1 &2 &k\end{pmatrix}.

(i) Calculate

\det\bigl(B(k)\bigr)

in terms of

k

. (ii) Determine all integer values of

k

in the interval

[-3,3]

for which

B(k)

is invertible. (iii) For

k=1

, find

B(1)^{-1}