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# Matrix question

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1. Part a I found fine thanks to earlier help but part b is confusing.

I tried to use determinant to guide me but to no avail.

How do I do this? It's only worth one mark so I feel like I'm missing something easy.
2. (Original post by Ravster)

Part a I found fine thanks to earlier help but part b is confusing.

I tried to use determinant to guide me but to no avail.

How do I do this? It's only worth one mark so I feel like I'm missing something easy.
If you multiply a 2x2 matrix by the 2x2 identity matrix you end up with the same matrix.

As A^n is just doing the transformation n times, what it's really asking you is how many times do you need to carry out the transformation to get back to where you started.
3. (Original post by Ravster)

Part a I found fine thanks to earlier help but part b is confusing.

I tried to use determinant to guide me but to no avail.

How do I do this? It's only worth one mark so I feel like I'm missing something easy.
If you have some coordinates and you multiply it by the identity matrix I, you will get the same thing: .

As A is the rotation about the origin by certain angle, how many times will it have rotate by that angle to get to its original position

Edit: Zacken has pointed out that you would have to get to multiple of which would be the LCM of the angle you found in part(a) and 360.
4. (Original post by Ravster)

Part a I found fine thanks to earlier help but part b is confusing.

I tried to use determinant to guide me but to no avail.

How do I do this? It's only worth one mark so I feel like I'm missing something easy.
Think about what the angle of rotation A represents and think about how many multiples of that rotation you need to get to a multiple of 360 degrees, which will be the identity matrix.

Remember that if A represents a rotation of then is a rotation of followed by a rotation of for a total rotation of . In general here is a rotation of degrees. So you need to find a s,t is a multiple of 360.
5. (Original post by shivtek)
Part was 135 I think. Or 45. I can't remember. I is the identity as you know so what it's asking is how many times does one apply A to get back to the start. So you do 360/(135 or 45). I got 8/3 I think
(Original post by Kvothe the arcane)
If you have some coordinates and you multiply it by the identity matrix I, you will get the same thing: .

represents a transformation and it's saying that

As A is the rotation about the origin by certain angle, how many times will it have rotate by that angle to get to its original position
I'm going to have to butt in here and say that you want a natural ; so is incorrect. You don't want to rotate to get to but rather, you want to rotate to get to a natural multiple of . Which is an important point here.
6. (Original post by Zacken)
...
That makes sense. You can't have a fraction of a multiplication. It would have made sense to evaluate a.
Thanks for pointing it out.
7. (Original post by Zacken)
I'm going to have to butt in here and say that you want a natural ; so is incorrect. You don't want to rotate to get to but rather, you want to rotate to get to a natural multiple of . Which is an important point here.
Away good point I didn't read "positive integer"
So really, raising it to the power of 8 would work, as it would be 0 rotation modulo 360. Thanks for pointing that out!
8. (Original post by shivtek)
Away good point I didn't read "positive integer"
So really, raising it to the power of 8 would work, as it would be 0 rotation modulo 360. Thanks for pointing that out!
Yep, 8 is the only correct answer here since it specifies being the smallest positive integer satisfying the condition. Right on with the rotation 0 modulo 360!

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