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If A=((1,2),(0,1)) P=((cos theta , sin t...

If `A=((1,2),(0,1))` `P=((cos theta , sin theta),( -sin theta, cos theta))`, `Q=P^T AP` find `PQ^(2014)P^T`

Text Solution

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`Q=P^TAP`
`QP^T=P^TAPP^T`
`QP^T=P^TA`
`PQ^2014 P^T=PQ^2013QP^T=PQ^2013P^TA`
`=PQ^2012QP^TA=PQ^2012P^TA^2`
`=PW^2011QP^TA^2=PQ^2011P^TA^3`
`=PP^TA^2014=IA^2014=A^2014`.
`A=[[1,2],[0,1]]`
...
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