The system of linear equations aligned x + y - z &= 0 x - y - z &= 0 x + y - z &= 0…

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

The system of linear equations

\begin{aligned} x + \lambda y - z &= 0 \\ \lambda x - y - z &= 0 \\ x + y - \lambda z &= 0 \end{aligned}

has a non-trivial solution for (1) exactly one value of

\lambda

(2) exactly two values of

\lambda

(3) exactly three values of

\lambda

(4) infinitely many values of

\lambda