Recent content by shaon0

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Thanks RGV. I've actually devised a less memory draining way by writing U as a generic upper triangular matrix which I presume is the way the Cholesky decomposition was devised.

Homework Statement Nullity(B-5I)=2 and Nullity(B-5I)^2=5 Characteristic poly is: (λ-5)^12 Find the possible jordan forms of B and the minimal polynomials for each of these JFs. The Attempt at a Solution JFs: Jn1(5) or ... or Jni(5). Not sure how to find these jordan forms and minimal polynomials.

Homework Statement See Attachment. Homework Equations x^TAx where x=<x,y,z> and A is some 3x3 matrix The Attempt at a Solution See Attachment. From here i have found the eigenvalues and vectors. What should I do next?.\

Ok, thanks Vela.

Ok, thanks. I think I've got it.

So; proje1v1? for all combinations of e1,e2,e3 and v1, v2?

Sorry vela, I've attached my working on this msg.

I've tried to use the projWv=projv1v+projv2v where v1=(-2,,1,-2)^T and v2=(1,4,-8)^T but i don't get the correct answer. Maybe because v1, v2 are not mutually orthogonal?

T[(1,5);(1,6)]=[(-2,5);(1,2)]. a1+5a2=-2;a1+6a2=1;a3+5a4=5 and a3+6a4=2 where T[(a1,a3);(a2;a4)] [(1,5);(1,6)|(-2,1)] and [(1,5);(1,6)|(5,2)] which gives me, T=[(-13,28);(11,-23)] which is not correct.

-2[1,5]+5[1,6]=[3,-4] and 1[1,5]+2[1,6]=[3,13] Basis: {[3,-4];[3,13]}

Wow! Thanks a lot, it's so much clearer now :) Would you happen to know what to do for 6b). I've tried the same approach you suggested for the other question but didn't get the right answer.

For P, the projection of what vector onto W? Would I just span the vectors I've found so, P=span{v1,v2} and find the co-effs s.t Basis1=a1.v1+a2.v2 where v1,v2 are the vectors I've found using the projection formula and a1,a2 are constants which will give me the 1st column of P?

Not too sure why you can't use that limit definition. Alternatively, the max values for f are for even n and min values are for odd n. And, it's easy to see that the sequence is decreasing. (this can be easily proven by ratios of coeffs). So now you can deduce what the max and min values for the...

1. Homework Statement See Attachment. Help with b) c) will be appreciated. 3. The Attempt at a Solution For the third question, my approach is sub in values for a and b which correspond to the co-effs. of the given basis. Then assemble a matrix from them. Eg...