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+1 vote
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in Matrices & determinants by (41.3k points)

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to

(A) 2

(B) -1

(C) 0

(D) 1

1 Answer

+1 vote
by (41.5k points)
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Best answer

Answer is (D) 1

 The system of equations x - cy - bz = 0, cx - y + az = 0 and bx + ay - z = 0 have non-trivial solution if

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