Linear Algebra: Rotation Matrix Qθ+φ

[camchetan]

Show that a rotation by θ followed by a rotation by φ can be expressed as either
two consecutive rotations, or one rotation of (θ + φ). That is, show that Qθ Qφ = Qθ+φ, where Q is the rotation matrix.

Can anyone answer this question I'm a beginner in Linear Algebra

 

[micromass]

What is the rotation matrix with angle $\theta$??

 

[genericusrnme]

do the matrix multiplication and see what happens

 

[HallsofIvy]

What is the rotation matrix with angle $\theta$??

do the matrix multiplication and see what happens

You will need the trig identities $cos(\theta+ \phi)= cos(\theta)cos(\phi)- sin(\theta)sin(\phi)$ and $sin(\theta+ \phi)= sin(\theta)cos(\phi)+ cos(\theta)sin(\phi)$