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Maths-

General

Easy

Question

The system of equations $lambda x plus y plus z equals 0 comma$ $negative x plus lambda y plus z equals 0 comma$ $negative x minus y plus lambda z equals 0$ , will have a non zero solution if real values of $lambda$ are given by

0
1
3
$\sqrt{3}$

The correct answer is: 0

Accordingly, $open vertical bar table row lambda 1 1 row cell negative 1 end cell lambda 1 row cell negative 1 end cell cell negative 1 end cell lambda end table close vertical bar equals 0 rightwards double arrow lambda to the power of 3 end exponent plus 3 lambda equals 0$
Therefore $lambda equals 0$ , since $lambda equals i square root of 3$ does not exist.

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