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Matrix help

I just can't seem to work out how to solve this :/ . Anyone care to solve this problem and explain?

Thanks! :smile:
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Reply 1
Avatar for B_9710
B_9710
18
Original post by abccba120
I just can't seem to work out how to solve this :/ . Anyone care to solve this problem and explain?

Thanks! :smile:


Have you found A3 \mathbf{A} ^3 in terms of t?
Reply 2
Avatar for abccba120
abccba120
OP
8
Original post by B_9710
Have you found A3 \mathbf{A} ^3 in terms of t?


No, is that what I need to do? How do I go about finding A3 \mathbf{A} ^3 in terms of t ..
Reply 3
Avatar for math42
math42
20
Original post by abccba120
No, is that what I need to do? How do I go about finding A3 \mathbf{A} ^3 in terms of t ..


Just do matrix multiplication in the normal way (A*A = A^2, then A*A^2 = A^3)
Original post by abccba120
...


Perhaps worth mentioning, if you've covered determinants, that

det(I3)=1det(I_3) = 1

So,
det(At3)=1det(A^3_t) = 1 and thus assuming your matrix is real

det(At)=1det(A_t) = 1 .............(1)

You can use this to check your result.

In itself though, it is insufficient to find the value of t, since (1) is satisified by two values of t, only one of which yields the identity matrix when cubed.
Original post by ghostwalker
Perhaps worth mentioning, if you've covered determinants, that

det(I3)=1det(I_3) = 1

So,
det(At3)=1det(A^3_t) = 1 and thus assuming your matrix is real

det(At)=1det(A_t) = 1 .............(1)

You can use this to check your result.

In itself though, it is insufficient to find the value of t, since (1) is satisified by two values of t, only one of which yields the identity matrix when cubed.


The determinant wouldn't be of much use here because the determinant being 1 only indicates that there is no change in volume nor reflection. It says nothing about the rotation that the original matrix may assume, and the identity matrix is very specific that there is no rotation, reflection or sheering/stretching in any directions.
Original post by RDKGames
The determinant wouldn't be of much use here because the determinant being 1 only indicates that there is no change in volume nor reflection. It says nothing about the rotation that the original matrix may assume, and the identity matrix is very specific that there is no rotation, reflection or sheering/stretching in any directions.


I do get the impression that you didn't actually read my post - I suggested it as a way to check an answer, not a means to derive it.
Original post by ghostwalker
I do get the impression that you didn't actually read my post - I suggested it as a way to check an answer, not a means to derive it.


I did. I'm simply giving the geometrical interpretation for the OP of what is happening with your method.
Reply 8
Avatar for Ano123
Ano123
15
Original post by RDKGames
I did. I'm simply giving the geometrical interpretation for the OP of what is happening with your method.


Mate, Ghostwalker is a big boy round these ends, don't f**k with him. He's been doing maths before you were even born.
Original post by Ano123
Mate, Ghostwalker is a big boy round these ends, don't f**k with him. He's been doing maths before you were even born.


He must be easily triggered if that's considered 'f**cking' with him. :h:
Reply 10
Avatar for alow
alow
19
Original post by RDKGames
He must be easily triggered if that's considered 'f**cking' with him. :h:


Although you clearly didn't read his post. He never said it was to find the answer, just check it.
Original post by alow
Although you clearly didn't read his post. He never said it was to find the answer, just check it.


I just wanted to put out some sort of geometrical interpretation linking to the original matrix and why it wouldn't work. Since he mentioned determinants it was suitable to respond to that and I might've mis-worded my response in the process, he's not wrong and I understood what he said. No need to be picky, let's just appreciate the fact that we're helping OP. :colonhash:

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