Let C( )= pmatrix 1 & 2 & 0 & & 3 & 1 & 4 pmatrix

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

Problem

Let

C(\lambda)=\begin{pmatrix}1 & 2 & \lambda \\ 0 & \lambda & 3 \\ \lambda & 1 & 4\end{pmatrix},

where

\lambda\in\mathbb R

. (i) Evaluate

\det\bigl(C(\lambda)\bigr)

as an explicit expression in

\lambda

. (ii) Hence determine all real values of

\lambda

for which

C(\lambda)

is invertible.