Question

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

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

Answer 1

Answer: (C)

For infinite solutions, $\left|\begin{array}{ccc}1& p& 0\\ 0& 1& p\\ p& 0& 1\end{array}\right|=1+p^3=0$
Hence, $p=-1$