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
How do we know the unit vector is v? and is it always eigenvalue to the power of n?
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 :/
When you say general solutions, do you mean putting x,y and z in terms of parameters when three simultaneous equations have an infinite number of solutions?
When you say general solutions, do you mean putting x,y and z in terms of parameters when three simultaneous equations have an infinite number of solutions?
in the past paper from june 2011 question 4i, i don't understand how the plus/minus has been taken out of the ln(x+-r(x^2-1)). what proves the negative is invalid?
in the past paper from june 2011 question 4i, i don't understand how the plus/minus has been taken out of the ln(x+-r(x^2-1)). what proves the negative is invalid?
since y>=0 then e^y>=1 and hence if it was x - r(x^2 - 1) then that would be smaller than 1.
I'm sure you'll be fine, you certainly seem to know your stuff anyway!
Thats impressive! Congratulations on getting an offer, thats really amazing! And hmm, ive worked hard but i get caught out on the simplest of things. Please can you help me with the question above?
Thank you so much! Do you always divide top and bottom by highest power of cos? Or is it sometimes sin? Sorry, its something im worrying about now
yeah you normally just do that and it works out nicely. it will hardly ever be sin because then you get cot(theta) which is harder to sort out afterwards.