Let F(α )=⎣⎡cosα sinα 0−sinα cosα 0001⎦⎤, where α∈R. Then [F(α ) ] −1 is equal to

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

Question

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

F (- α)

F (α^{- 1})

F (2 α)

None of these

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Scarlett Discussed

Let

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

, where

α \in R

. Then

[F (α)]^{- 1}

is equal to

11 mins ago

Discuss this question LIVE

11 mins ago

Now,

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

∴ F (α) F (- α) = ⎣ ⎡ 100010001 ⎦ ⎤ = I

∴ F (- α) = [F (α)]^{- 1}

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Question Text	Let $F (α) = ⎣ ⎡ cos α sin α 0 - sin α cos α 0 001 ⎦ ⎤$ , where $α \in R$ . Then $[F (α)]^{- 1}$ is equal to
Answer Type	Text solution:1
Upvotes	150