A - - - cos- sin- 0-sin- cos- 00 0 e- - - A - - -1-

A( ,β)=[ cos amp; sin amp; 0; sin amp; cos amp; 0; 0 amp;0 amp;e^β nbsp; ] A^ 1=[ cos amp; sin amp; 0; sin amp; co ...

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Sin(A+B)Sin(A-B)

A α ,β = cosα...

Question

$A (α, β) = ⎛ ⎜ ⎝ \begin{matrix} c o s α & s i n α & 0 - s i n α & c o s α & 0 0 & 0 & e^{β} \end{matrix} ⎞ ⎟ ⎠ \Rightarrow {[A (α, β)]}^{- 1} =$

$A (- α, β)$

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$A (- α, - β)$

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$A (α, - β)$

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$A (α, β)$

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Solution

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A (α, β) = ⎡ ⎢ ⎣ \begin{matrix} cos α & sin α & 0 - sin α & cos α & 0 0 & 0 & e^{β} \end{matrix} ⎤ ⎥ ⎦

A (α, β)^{- 1}

A (α, β) = ⎡ ⎢ ⎣ \begin{matrix} c o s α & s i n α & 0 - s i n α & c o s α & 0 0 & 0 & e^{β} \end{matrix} ⎤ ⎥ ⎦

A ({α, β)}^{- 1}

A

If A $(α, β) = ⎡ ⎢ ⎣ \begin{matrix} c o s α & s i n α & 0 - s i n α & c o s α & 0 0 & 0 & e^{β} \end{matrix} ⎤ ⎥ ⎦, t h e n$

A (α, β) = ⎡ ⎢ ⎣ \begin{matrix} cos α & sin α & 0 - sin α & cos α & 0 0 & 0 & e^{β} \end{matrix} ⎤ ⎥ ⎦

A (α, β) = ⎡ ⎢ ⎣ \begin{matrix} cos α & sin α & 0 - sin α & cos α & 0 0 & 0 & e^{β} \end{matrix} ⎤ ⎥ ⎦

(A (α, β))^{- 1}

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