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Matrix question Watch

1. Two matrices A and B are given by

.

One is a reflection and the other a rotation. Suppose X is the rotation matrix and Y is the reflection matrix, determine which of A and B is the rotation and which is the reflection.

I honestly have no idea how to start this problem. Any initial shove in the right direction would be appreciated.
2. (Original post by Music99)
Two matrices A and B are given by

.

One is a reflection and the other a rotation. Suppose X is the rotation matrix and Y is the reflection matrix, determine which of M and N is the rotation and which is the reflection.

I honestly have no idea how to start this problem. Any initial shove in the right direction would be appreciated.
Not sure what X, Y, M and N are meant to be, but one way to approach this would be to think about determinants.
3. (Original post by Mark13)
Not sure what X, Y, M and N are meant to be, but one way to approach this would be to think about determinants.
Opps wrote out a wrong bit see the edit. . I think X and Y are just meant to be a general rotation and reflection in 3 dimensions.
4. Well a pure rotation matrix in 3D has an eigenvalue of 1, amongst other things, yet neither of A, nor B does.

Unless I made another slip!

Edit: Made a slip. First has an eigenvalue of 1.
5. (Original post by ghostwalker)
Well a pure rotation matrix in 3D has an eigenvalue of 1, amongst other things, yet neither of A, nor B does.

Unless I made another slip!
We haven't covered eigenvalues yet. I'm not too sure all the question says is Suppose X is the rotation matrix and Y is the reflection matrix. Determine which of A and B is the rotation and which is the reflection.
6. (Original post by Music99)
We haven't covered eigenvalues yet. I'm not too sure all the question says is Suppose X is the rotation matrix and Y is the reflection matrix. Determine which of A and B is the rotation and which is the reflection.
Have you posted the question exactly as stated? there doesn't seem to be any need for the clause beginning "Suppose X..." - surely it could just ask which of A and B is the rotation and which is the reflection???
7. (Original post by davros)
Have you posted the question exactly as stated? there doesn't seem to be any need for the clause beginning "Suppose X..." - surely it could just ask which of A and B is the rotation and which is the reflection???
That's what I thought, maybe it's missing a bit of info? The exact wording is

The matrices A and B are given by:

And gives the matrices I gave above. One is a reflection and the other a rotation. Suppose X is the rotation matrix and Y is the reflection matrix. Determine which if A and B is the rotation and which is the reflection.
8. Bump.
9. (Original post by Music99)
Bump.
Could you do a scan of the page? It still seems confusing with the X, Y.
10. (Original post by ghostwalker)
Could you do a scan of the page? It still seems confusing with the X, Y.
Yeah sure, I just realized I used A and B for the matrices instead of M and N. I think maybe not all the question printed or something
11. (Original post by Music99)
Yeah sure, I just realized I used A and B for the matrices instead of M and N. I think maybe not all the question printed or something
I think you can try, if a matrix represents a reflection, then squaring it should give you the identity matrix.
12. (Original post by ghostwalker)
I think you can try. If a matrix represents a reflection, then squaring it should give you the identity matrix.
I'll give that a try, the X and Y thing is just weird.
13. (Original post by Music99)
I'll give that a try, the X and Y thing is just weird.
Sorry, just realised that seemed a bit arrogant. I put in a full stop thoughtlessly.
14. (Original post by ghostwalker)
Sorry, just realised that seemed a bit arrogant. I put in a full stop thoughtlessly.
It's cool. Okay so I did that and got the 2nd matrix as the reflection, how did you know that squaring it like that would work?
15. Oh I thought this was a question about the film The Matrix

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16. (Original post by holson)
Oh I thought this was a question about the film The Matrix
It is not "the one", Zathrus. (To mix my universes)
17. (Original post by holson)
Oh I thought this was a question about the film The Matrix

Posted from TSR Mobile
XD! If only. That would be epic, Neo you must work out the optimal punching angle to hit agent smith in the face .
18. (Original post by Music99)
It's cool. Okay so I did that and got the 2nd matrix as the reflection, how did you know that squaring it like that would work?
A reflection of a reflection takes you back to where you started. Hence....

It's not a definitive test as repeating a rotation of 180 degrees would do the same thing.

But if you know one isn't a reflection and the square of one isn't the identity matrix, then that's the one that isn't a reflection.
19. (Original post by ghostwalker)
A reflection of a reflection takes you back to where you started. Hence....

It's not a definitive test as repeating a rotation of 180 degrees would do the same thing.

But if you know one isn't a reflection and the square of one isn't the identity matrix, then that's the one that isn't a reflection.
Ah right that makes sense thank you!. If I get stuck on other parts is it okay if I quote you?
20. (Original post by Music99)
If I get stuck on other parts is it okay if I quote you?
Sure. Can't guarantee I'll be able to help though.

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