Q46 / 124 · NTA Abhyas (JEE Main) 2020 · Mathematics · Determinants

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

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

Solution

For infinite solutions,

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

Hence,

p = - 1

Hence, the correct answer is option: 'C'.

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