Question

Let A = [cos θ -sin θ] x= [x1] y= [y1]
[sin θ cosθ] [x2] [y2]
Explain geometrically Ax=y if
A = [cosθ 0 -sinθ]
[0 1 0]
[sinθ 0 cosθ]?
(Note: These are matrices mentioned above.)

Answer 1

This matrix is a rotation. When is a vector y equal to x having being rotated by an angle of theta?