First slide

System of linear equations

Question

The value of a for which the system of equations ax + y + z = 0, x + ay + z = 0, x + y + z = 0, possess non-zero solutions are given by,

Moderate

A

2
B

0
C

1
D

None of these

Solution

The set of homogeneous equations will have a nonzero solution if $∆ = 0$
$i . e ., |\begin{matrix} a & 1 & 1 \\ 1 & a & 1 \\ 1 & 1 & 1 \end{matrix}| = 0$
⇒ a = 1

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