Question on Groups concerning matrices...
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Question on Groups concerning matrices...Let M denote the set of real 2x2 matrices of the form
where x and y are not both zero,
M=
Show that M is a group under matrix multiplication. (you may assume that matrix multiplication is associative)
I am just confused about something, I am trying to figure if for example this is multiplication of the form:
or if the operation has to be of the form
,
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nevermind, i messed up on something really simple...
Last edited by The Racist Dragon; 07-04-2012 at 15:45. -
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Re: Question on Groups concerning matrices...It's safe to assume that
is a group since the question asks you to show that it is, it doesn't ask whether or not it is.
If your example of
didn't work then you must have multiplied your matrices wrong.
The closure property is this: if
then 
.
So suppose
and 
, with 
and 
. Show that 
can be written in the form 
and that 
(where 
are in terms of 
).
P.S.: To fix your LaTeX code, take the { symbols off the start of each of the lines.Last edited by nuodai; 07-04-2012 at 14:29. -
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Re: Question on Groups concerning matrices...Ah thanks, coding fixed now(Original post by nuodai)
It's safe to assume that is a group since the question asks you to show that it is, it doesn't ask whether or not it is.
If your example of didn't work then you must have multiplied your matrices wrong.
The closure property is this: if then .
So suppose and , with and . Show that can be written in the form and that (where are in terms of ).
P.S.: To fix your LaTeX code, take the { symbols off the start of each of the lines.
I actually worked out 2x3 + (1x-2) as being 9 for some reason in my counterexample which is why it confused me :s but my counterexample actually does conform to the group rules
