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+1 vote
13.8k views
in Mathematics by (53.3k points)

If  A = 1/3[(1,2,2)(2,1,-2),(a,2,b)] is an orthogonal matrix, then

(a)  a = 2, b = 1 

(b)   a = –2, b = –1 

(c)   a = 2, b = –1 

(d)  a = –2, b = 1

1 Answer

+2 votes
by (53.1k points)
selected by
 
Best answer

Correct option  (b)  a = –2, b = –1

Explanation:

AAT = I

⇒ a + 4 + 2b = 0,

2a + 2 – 2b = 0 & a+ 4 + b2 = 9 gives a = –2, b = –1. 

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