If A - - - cos- sin- 0- -sin- cos- 0- 0 0 e- - then

We have (A ( α ,β ) )'=[ cosα nbsp; amp; sinα nbsp; nbsp; amp;0; nbsp; nbsp;sinα amp;cosα nbsp; nbsp; amp;0; nbsp; ...

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Inverse of a Matrix

If A α ,β =[ ...

Question

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

{(A (α, β))}^{'} = A (- α, β)

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{(A (α, β))}^{- 1} = A (- α, - β)

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Adj (A (α, β)) = e^{β} A (- α, - β)

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{(A (α, β))}^{'} = A (α, - β)

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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

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

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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