# FP1 Invariant PointsWatch

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#1
Hi, I was wondering if anyone could help me with finding invariant points. The question is to find the invariant points for transformations of the following matrix:

Here's what I did:

=

=

This is the only method I can figure out of solving it, and as far as I can tell I've made no mistakes, but then the answer given in the book is (, -), and I can't for the life of me figure out what Lambda is supposed to represent! Can somebody please explain this, and if I've not solved this properly, I'd really appreciate a step-by-step solution if anyone can spare the time. Thanks in advance! <3 xoxo
0
5 years ago
#2
take the corresponding entries in the top "row" - OR: which implies that the solution is points of the form

or, as they put it:

(the lower rows equated just confirms the top one, once you sub y=-x into it)

they just use lambda as it is arbitrary, to let you see that the solution is any one number, the y of which is the negation.
0
5 years ago
#3
(Original post by mattallica)
Hi, I was wondering if anyone could help me with finding invariant points. The question is to find the invariant points for transformations of the following matrix:

Here's what I did:

=

=

This is the only method I can figure out of solving it, and as far as I can tell I've made no mistakes, but then the answer given in the book is (, -), and I can't for the life of me figure out what Lambda is supposed to represent! Can somebody please explain this, and if I've not solved this properly, I'd really appreciate a step-by-step solution if anyone can spare the time. Thanks in advance! <3 xoxo
just indicates that it is a line of invariant points. You could just have correctly given it as (k,-k) or (t,-t) the letter used is arbitrary.
0
#4
(Original post by brianeverit)
just indicates that it is a line of invariant points. You could just have correctly given it as (k,-k) or (t,-t) the letter used is arbitrary.
So if I was to say (, ) would that just be the same as x=y?
0
5 years ago
#5
(Original post by mattallica)
So if I was to say (, ) would that just be the same as x=y?
Yes
0
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