Question

If A= `[(cos α, -sin α), (sin α, cos α)]` then A + A' = I then the value of α is  ______.

पर्याय

• `pi/6`

• `pi/3`

• `pi`

•  `(3pi)/2`

Answer 1

If A = `[(cos α, -sin α), (sin α, cos α)]` then A + A' = I then the value of α is  `underlinebb(pi/3)`.

Explanation:

A = `[(cos α, -sin α),(sin α, cos α)]`, A' = `[(cos α, sin α),(-sin α, cos α)]`

∴ A + A' = I

`[(cos α, -sin α),(sin α, cos α)] + [(cos α, sin α), (-sin α, cos α)] = [(1, 0), (0, 1)]`

⇒ `[(cos α + cos α, -sin α + sin α), (sin α - sin α, cos α + cos α)] = [(1, 0),(0, 1)]`

⇒ `[(2 cos α, 0), (0, 2 cos α)] = [(1, 0), (0, 1)]`

⇒ `2 cos α = 1/2`

⇒ `cos α = cos pi/3`

∴ `α = pi/3`