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

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

NTA AbhyasNTA Abhyas 2020Matrices

Solution:

For infinite solutions, $\begin{vmatrix} 1 & p & 0 \\ 0 & 1 & p \\ p & 0 & 1 \end{vmatrix}=1+p^{3}=0$
Hence, $p=-1$