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# Matrix multiplication

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1. Let A(pheta)= (row1: cos(pheta), sin(pheta) row 2: -sin(pheta), cos (pheta) )

Prove A(pheta)A(alpha)= A(pheta+alpha)

So for the LHS by multiplying matrices I got (row 1: cos(pheta)cos(alpha) -sin (pheta)sin(alpha), -sin(pheta)cos(alpha)-cos(pheta)sin(alpha) row 2: cos(pheta)sin(alpha) + sin(pheta)cos(alpha), -sin(pheta)sin(alpha) + cos(pheta)cos(alpha))

On the RHS I got (row 1: cos(pheta+alpha, sin(pheta +alpha), row 2 -sin(pheta+alpha), cos (pheta+Alpha))

Am I approaching this question in the right way, and if so where would i go from here?
2. Look in your formula book at the compound angle formulae?

Theta by the way.
3. Maybe i'm missing something here, but aren't you done at this point?

Just be multiplying them directly you've ended with the RHS = which is what you were looking for.
4. (Original post by Rubgish)
Maybe i'm missing something here, but aren't you done at this point?

Just be multiplying them directly you've ended with the RHS = which is what you were looking for.
I don't think he recognised the compound angle formulae at all. He just wrote down the expected answer. It would have fooled me (and everyone else) though!
5. (Original post by Mr M)
I don't think he recognised the compound angle formulae at all. He just wrote down the expected answer. It would have fooled me (and everyone else) though!
Ah reading back through it, it does seem that way. I skimmed it too quickly first time round!
6. (Original post by Mr M)
Look in your formula book at the compound angle formulae?

Theta by the way.
Thank you, oh it actually does work. Thought I was approaching it wrong.

It then says give a geometrical intepretation of the transformation represented by A.
Don't suppose you have any ideas on how to answer that?
7. Yes. The fact that angles are involved might be a massive clue.
8. (Original post by Mr M)
I don't think he recognised the compound angle formulae at all. He just wrote down the expected answer. It would have fooled me (and everyone else) though!
Yeah i completely forgot about the compound formula, I didn't expect it to come up for my vectors module, but it is
9. (Original post by Mr M)
Yes. The fact that angles are involved might be a massive clue.
Thank you for all your help.
Honestly no, I have no idea.
10. Thank you for the link!

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