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Year 13 Maths Help Thread

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how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

Thanks
Original post by Daiblain
how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

Thanks


Sorry, I either don't understand the question, or I don't think you gave enough information there. I think it's the latter.
Original post by Daiblain
how can three equations of x+y+z = 0 formed from a matrix give an eigenvector of (p, q, -p-q)?

Thanks

Well all three equations agree if x=p, x=p, y=q y=q then p+q+z=0 p+q+z=0 so of course z=−p−q z=-p-q .
Do you notice that there are many solutions you can try, say (α−α0) \begin{pmatrix} \alpha \\ -\alpha \\ 0 \end{pmatrix} or (ββ−2β) \begin{pmatrix} \beta \\ \beta \\ -2\beta \end{pmatrix} . You actually get an eigenplane, and the eigenplane has equation x+y+z=0 x+y+z=0 and you can parametrise the plane in anyway you want if you want it in parametric form. All you would do is add any two linearly independent eigenvectors to get it in parametric form.
(edited 7 years ago)
Original post by RDKGames
Sorry, I either don't understand the question, or I don't think you gave enough information there. I think it's the latter.


Original post by B_9710
Well all three equations agree if x=p, x=p, y=q y=q then p+q+z=0 p+q+z=0 so of course z=−p−q z=-p-q .
Do you notice that there are many solutions you can try, say (α−α0) \begin{pmatrix} \alpha \\ -\alpha \\ 0 \end{pmatrix} or (ββ−2β) \begin{pmatrix} \beta \\ \beta \\ -2\beta \end{pmatrix} . You actually get an eigenplane, and the eigenplane has equation x+y+z=0 x+y+z=0 and you can parametrise the plane in anyway you want if you want it in parametric form. All you would do is add any two linearly independent eigenvectors to get it in parametric form.


Sorry, It's my fault Matrix with eigenvalue 5 is (-211)(1-21)(11-2) to give -2x+y+z = 0, x-2y+z =0 and x+y-2z=0I eliminated one variable to make x=y=z because I can't really see it off the bat, making the eigenvector (x,x,x) -> x(1,1,1)With eigenvalue 2 you get(111)(111)(111)to give x+y+z=0all of this was taken off the mei fp2 book, i just didnt understand the eigenvector that goes with the last matrixThanks a bunch!
Yeah, the post came out great
Reply 505
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Term hasn't even started and yet the thread already has 10% of the posts that the Year 12 thread had.

Speaking of the Year 12 thread, time for me to bump it!
Reply 506
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Are all summations of the form ∑r=1∞1ar+b\sum^{\infty}_{r=1} \frac{1}{ar+b} where a,b∈Ra,b \in \mathbb{R} divergent?
(edited 7 years ago)
Original post by Palette
Are all 'things' of the form ∑r=1∞1ar+b\sum^{\infty}_{r=1} \frac{1}{ar+b} where a,b∈Ra,b \in \mathbb{R} divergent?


Yes - take out a factor of (1/a) and you get the sum from 1 to infinity of (1/(x+(b/a)) - which is just a shift of the sum of 1/x - which with these limits we know diverges
(and in the case a=0 you just have an infinite number of '1/b's added together which must diverge)
(edited 7 years ago)
Reply 508
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Original post by ValerieKR
Yes - take out a factor of (1/a) and you get the sum from 1 to infinity of (1/(x+(b/a)) - which is just a shift of the sum of 1/x - which we know diverges
(and in the case a=0 you just have an infinite number of '1/b's added together which must diverge)

Thanks for the help; do you mind if I add your name to the helpers list?
(edited 7 years ago)
Original post by Palette
Thanks for the help; would you mind if I add your name to the helpers list?


What responsibility does being one involve?
Reply 510
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Original post by ValerieKR
What responsibility does being one involve?


Nothing more than what you're currently doing.
Original post by Palette
Nothing more than what you're currently doing.


Ok - sure
How do u integrate 1/x^2+1
Original post by youreanutter
How do u integrate 1/x^2+1


Use sub x=tan⁡θ x=\tan \theta .
Original post by B_9710
Use sub x=tan⁡θ x=\tan \theta .


Is that a c4 method?
Original post by youreanutter
Is that a c4 method?


This integral is not expected is C4 but you can still apply normal substitution methods.
Do we need to remember the harmonic identities? Or do we get given them in the question?
Original post by jamestg
Do we need to remember the harmonic identities? Or do we get given them in the question?


http://www.mathsnetalevel.com/download/Edexcel_formula_book.pdf#page=8
Original post by SeanFM


Thanks! I'm sure I printed off this haha, probably stored it away with all my AS work...

Looks like I'm going to have to get revising :biggrin:
Original post by jamestg
Thanks! I'm sure I printed off this haha, probably stored it away with all my AS work...

Looks like I'm going to have to get revising :biggrin:
If you've done it right you won't need the formula book for any trig identities :wink: but it's nice to have. You'll be fine anyway from your AS results :tongue:

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