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Let A = 0   2 y   z x   y - z x - y   z such that A T A = I , then the value of x 2 + y 2 + z 2 is

Correct answer

1

Step-by-step solution

A T = 0 x x 2 y y - y z - z z A T A = 0 x x 2 y y - y z - z z 0 2 y z x y - z x - y z = 2 x 2 0 0 0 6 y 2 0 0 0 3 z 2 = 1 0 0 0 1 0 0 0 1 A T A = I 2 x 2 = 1 ⇒ x 2 = 1 2 3 z 2 = 1 ⇒ z 2 = 1 3 6 y 2 = 1 ⇒ y 2 = 1 6 x 2 + y 2 + z 2 = 1 2 + 1 3 + 1 6 = 1 2 + 1 2 = 1

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