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Let F( )={bmatrix} cos & -sin & 0 sin & cos & 0 0 & 0 &

Question

Let $F (α) = ⎣ ⎡ cos α s in α 0 - s in α cos α 0 001 ⎦ ⎤$ , where $α ϵ R$ . Then $(F (α))^{- 1}$ is equal to

F (α)^{- 1}

F (- α)

F (2 α)

none of these

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Noah Discussed

Let

F (α) = ⎣ ⎡ cos α s in α 0 - s in α cos α 0 001 ⎦ ⎤

, where

α ϵ R

. Then

(F (α))^{- 1}

is equal to

11 mins ago

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11 mins ago

Text solutionVerified

Given,

F (α) = A = ⎣ ⎡ cos α sin α 0 - sin α cos α 0 001 ⎦ ⎤

\Rightarrow ∣ A ∣ = cos^{2} α + sin^{2} α = 1

a d j A = C^{T} = ⎣ ⎡ cos α sin α 0 - sin α cos α 0 001 ⎦ ⎤^{T}

\Rightarrow a d j A = ⎣ ⎡ cos α - sin α 0 sin α cos α 0 001 ⎦ ⎤

Now,

A^{- 1} = ⎣ ⎡ cos α - sin α 0 sin α cos α 0 001 ⎦ ⎤

A^{- 1} = ⎣ ⎡ cos (- α) sin (- α) 0 - sin (- α) cos (- α) 0 001 ⎦ ⎤

\Rightarrow A^{- 1} = F (- α)

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Question Text	Let $F (α) = ⎣ ⎡ cos α s in α 0 - s in α cos α 0 001 ⎦ ⎤$ , where $α ϵ R$ . Then $(F (α))^{- 1}$ is equal to
Answer Type	Text solution:1
Upvotes	151