FP2 MEI OCR Official Thread - 23rd June 2014

Original post by pujah0ntas

Say you know the matrix, eigenvalue and its corresponding eigenvectors, what does 'State the magnitudes and directions of the vectors M2v and M−1v ' mean?

Is this from a past paper? :/

Reply 46

pujah0ntas

Original post by mathematigeek

Is this from a past paper? :/

Jan 2013
Q.3 part (iii)

Reply 47

Original post by pujah0ntas

Jan 2013
Q.3 part (iii)

This is the mei thread :/ either you got the wrong exam paper or the wrong thread. Jan 2013 on mei has nothing to do with that in 3 iii) sorry :/

Reply 48

Rex Regum

5

Has anyone got any mark scheme notes? i.e. pointers on certain questions which tend to be repeated in past papers or any difficult questions that you may have encountered and are worth understanding their procedures.

Reply 49

username1107833

Does anyone understand Q3)iii) in January 2011 well enough to explain it to me?

"State the magnitude of vector (M^n)*v", I just don't get it and these types of questions come up every once in a while. Thanks :smile:

Reply 50

Illiberal Liberal

Screen Shot 2014-06-22 at 18.46.14.png24.5KB

Original post by mathematigeek

This is the mei thread :/ either you got the wrong exam paper or the wrong thread. Jan 2013 on mei has nothing to do with that in 3 iii) sorry :/

She means the Jan 12 paper. :smile:

Reply 51

Original post by theCreator

Does anyone understand Q3)iii) in January 2011 well enough to explain it to me?

"State the magnitude of vector (M^n)*v", I just don't get it and these types of questions come up every once in a while. Thanks :smile:

Since v has magnitude 1 (unit vector) the magnitude of Mⁿv is simply the eigenvalue used to find the unit vector to the power n :smile:

Reply 52

Original post by Law-Hopeful

She means the Jan 12 paper. :smile:

Oh I see, I thought I'd seen it before! Thanks :')

Reply 53

username1107833

Original post by mathematigeek

Since v has magnitude 1 (unit vector) the magnitude of Mⁿv is simply the eigenvalue used to find the unit vector to the power n :smile:

So can you use this same method to answer 3)iii) in January 2012 too?

Reply 54

Original post by pujah0ntas

Say you know the matrix, eigenvalue and its corresponding eigenvectors, what does 'State the magnitudes and directions of the vectors M2v and M−1v ' mean?

Okay, so you know the unit vector is v, this has magnitude 1. You also know the eigen value is 5. This is now M since it satisfies the characteristics equation of M. So the magnitude of M²v is simply 1*5² so 25. The same method is applied to M^-1v giving magnitude 0.2. Both are in the direction of v since the eigen value is a scalar quantity.

Hope this helps

Reply 55

Original post by theCreator

So can you use this same method to answer 3)iii) in January 2012 too?

Yep

see post above ^^ :smile:

Reply 56

Rex Regum

5

Are there any other questions which may be sort of tricky like the M^2v posted above?

(edited 9 years ago)

Reply 57

Original post by Rex Regum

Are there any other questions which may sort of tricky like the M^2v posted above?

I actually find finding eigen vectors the hardest part of fp2, does anyone know a way to check if you got them right in the exam?

And as for tricky questions, with matrices, the only other tricky part is finding general solutions? Idk :/ and then other tricky parts are C+jS (recognising the type of series) and I find complex roots quite tricky. Calculus and polar curves is all about technique. Hyperbolics are nice too so yea :/

Reply 58

username1107833