The system of equations x + p y = 0 , y + p z = 0 and z + p x = 0 has infinitely many solutions for

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Question: Answered & Verified by Expert

The system of equations

x + p y = 0

,

y + p z = 0

and

z + p x = 0

has infinitely many solutions for

MathematicsDeterminantsJEE Main

Options:

A $p = 1$
B $p = 0$
C $p = - 1$
D no real value of $p$

Solution:

1199 Upvotes Verified Answer

The correct answer is:

p = - 1

For infinite solutions,

|\begin{matrix} 1 & p & 0 \\ 0 & 1 & p \\ p & 0 & 1 \end{matrix}| = 1 + p^{3} = 0

Hence,

p = - 1

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