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FP1 Question

Hi, can someone help me understand how to work this out?

Find the matrix M^2006

Where M =​
Original post by srepse
Hi, can someone help me understand how to work this out?

Find the matrix M^2006

Where M =​


Well, you may recognise that it's some form of rotation matrix, or just try working out a few powers of M.
Reply 2
Avatar for MathsSir
MathsSir
1
The matrix is a 45 deg anti-clockwise rotation.
(cos 45 sin 45
-sin 45 cos 45)
and every 8 applications gets you back to where you started.
2006/8 = 250+6/8, so the final matrix will be a 6x45=270 deg rotation.
So you finish up with
(cos 270 sin 270
-sin 270 cos 270)
or
0 -1
1 0

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