Question

The system of equations ax + y + z = a –1, x + ay + z

= a –1, x + y + az = a –1 has one solution, if a is

• A. –2
• B. Either –2 or 1
• C. Not –2
• D. 1

Answer 1

Answer: (A)

–2

Answer 2

D = $\left| \begin{matrix} \alpha & 1 & 1 \\ 1 & \alpha & 1 \\ 1 & 1 & \alpha \end{matrix} \right|$ = 0

Ž a = 1 or –2

But a ¹ 1, at a = 1, x + y + z = 0 and equation has infinite solutions.

So choice (1) is correct