If the following system has non-trivial solution, \(px + qy + rz = 0\) \(qx +…

GATE · 2015 · CS · Set 3 · Computer Science & IT

If the following system has non-trivial solution,

px+qy+rz=0px + qy + rz = 0

qx+ry+pz=0qx + ry + pz = 0

rx+py+qz=0rx + py + qz = 0

then which one of the following options is TRUE?

  1. A.

    p−q+r=0 or p=q=−rp - q + r = 0 \text{ or } p = q = -r

  2. B.

    p+q−r=0 or p=−q=rp + q - r = 0 \text{ or } p = -q = r

  3. C.

    p+q+r=0 or p=q=rp + q + r = 0 \text{ or } p = q = r

  4. D.

    p−q+r=0 or p=−q=−rp - q + r = 0 \text{ or } p = -q = -r

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