Question

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

Answer 1

Correct Answer - 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`