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If alpha, beta, gamma are three real num...

If `alpha, beta, gamma` are three real numbers and `A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)]`
then which of following is/are true ?

A

A is singular

B

A is symmetric

C

A is orthogonal

D

A is not invertible

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`A=[(cos alpha,sin alpha,0),(cos beta,sin beta,0),(cos gamma,sin gamma,0)][(cos alpha,cos beta,cos gamma),(sin alpha,sin beta,sin gamma),(0,0,0)]`
Clearly, A is symmetric and `|A|=0`, hence, singular and not invertiable. Also,
`A A^(T) ne 1`
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