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Question: The value of ‘a’ for which system of equation ax + y + z = 0, x + ay + z = 0 & x + y + z = 0 posses...

The value of ‘a’ for which system of equation

ax + y + z = 0, x + ay + z = 0 & x + y + z = 0 possesses non-

null solution is –

A

1, 2

B

1, – 1

C

1

D

None

Answer

1

Explanation

Solution

D = 0 ⇒ ∣a111a1111∣=0\left| \begin{matrix} a & 1 & 1 \\ 1 & a & 1 \\ 1 & 1 & 1 \end{matrix} \right| = 0 ⇒ ∣a011a−11101∣=0\left| \begin{matrix} a & 0 & 1 \\ 1 & a - 1 & 1 \\ 1 & 0 & 1 \end{matrix} \right| = 0 ⇒ (a – 1)

[a – 1] = 0 ⇒ a=1\begin{matrix} a = 1 \end{matrix}