Question

Let F(α) = `[(cosalpha, -sinalpha, 0), (sinalpha, cosalpha, 0), (0, 0, 1)]` where α ∈ R. Then [F(α)]^-1 is equal to ______ 

विकल्प

• F(-α)

• F(α^-1) 

• F(2α)

• None of these

Answer 1

Let F(α) = `[(cosalpha, -sinalpha, 0), (sinalpha, cosalpha, 0), (0, 0, 1)]` where α ∈ R. Then [F(α)]^-1 is equal to F(-α).

Explanation:

F(α) . F(-α)

`[(cosalpha, -sinalpha, 0), (sinalpha, cosalpha, 0), (0, 0, 1)] [(cosalpha, sinalpha, 0), (-sinalpha, cosalpha, 0), (0, 0, 1)]`

= `[(1, 0, 0), (0, 1, 0), (0, 0, 1)] = I`

∴ `[F(alpha)]^-1 = F(-alpha)`