Question

Given the system of equations px + y + z = 1,

x + py + z = p, x + y + pz = p². Then for what value of p does this system have no solution.

• A. 0
• B. 1
• C. 2
• D. – 2

Answer 1

Answer: (D)

– 2

Answer 2

∆ =$\left| \begin{matrix} p & 1 & 1 \\ 1 & p & 1 \\ 1 & 1 & p \end{matrix} \right|$= p(p² – 1) – 1(p – 1) + 1(1 – p) = 0

= (p – 1) [p(p + 1) – 2] = 0 ⇒  p = 1, –2

at p = 1 gives infinite many solution

at p = –2 at least one of (∆₁, ∆₂, ∆₃) are non zero