Q15: 15 A=cos αsin α-sin αcos α then Prove that Aa=cos ηαsin ηα-sin ηαcos ηα where η is - Maths - Matrices

Question

Q15:

15 A = cos   α sin   α - sin   α
cos   α   t h e n   P r o v e   t h a t
  A a = cos   η α sin   η α -
sin   η α cos   η α   w h e r e
  η   i s   a   p o s i t i v e   i n
t e g e r

Neha Sethi · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5ab0b02d6b889%20png">
Hence by PMI the result is valid  for any positive integer n
Regards

Q15: 15. A = cos α sin α - sin α cos α t h e n P r o v e t h a t A a = cos η α sin η α - sin η α cos η α w h e r e η i s a p o s i t i v e i n t e g e r .

Q15:

15. $A = [\begin{matrix} \cos α & \sin α \\ - \sin α & \cos α \end{matrix}] t h e n P r o v e t h a t A^{a} = [\begin{matrix} \cos η α & \sin η α \\ - \sin η α & \cos η α \end{matrix}] w h e r e η i s a p o s i t i v e i n t e g e r .$