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If the following system has non – trivial solution
px +qy + rz = 0
qx + ry + pz = 0
rx + py +qz = 0
then which one of the following options is TRUE ?
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- p – q +r = 0 or p = q = – r
- p + q – r = 0 or p = – q = r
- p + q +r = 0 or p = q = r
- p – q +r = 0 or p = – q = – r
- p – q +r = 0 or p = q = – r
Correct Option: C
For non-trivial solution, we have | A | = 0
⇒ (r – q)2 – (p – q) (p – r) = 0
⇒ p2 + q2 + r2 – pq – qr – pr = 0
⇒ (p – q)2 + (q – r)2 + (r – p)2 = 0
⇒ p – q = 0; q – r = 0, r – p = 0
⇒ p = q = r.
