Let A= pmatrix k & 1 & 1 1 & k & 1 1 & 1 & k pmatrix , B= pmatrix 6 6 6 pmatrix

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Let

A=\begin{pmatrix}k & 1 & 1\\1 & k & 1\\1 & 1 & k\end{pmatrix},\qquad B=\begin{pmatrix}6\\6\\6\end{pmatrix}.

(i) Show that

|A|=(k-1)^2(k+2)

. (ii) Find all real values of

k

for which

A

is invertible. (iii) For

k=2

, compute

A^{-1}

. (iv) Using the result of part (iii), solve the system

AX=B

when

k=2