I need to prove by induction that this 2x2 matrix:
[cosθ -senθ; senθ cosθ]^n is equal to this 2x2 matrix:
[cos(n)θ -sen(n)θ; sen(n)θ cos(n)θ] for all n ∈ Z.
Since it's by induction, I've already got the and , but... now what?
Thanks!
I need to prove by induction that this 2x2 matrix:
[cosθ -senθ; senθ cosθ]^n is equal to this 2x2 matrix:
[cos(n)θ -sen(n)θ; sen(n)θ cos(n)θ] for all n ∈ Z.
Since it's by induction, I've already got the and , but... now what?
Thanks!