Recent content by math222

ok got it. i basically ended up with a^2 + b^2. thanks again for your help.

ahhhh ok i'll try again, thanks for your help.

So do I assume that L(a*e1 + b*e2) is in fact similar? And I'm not sure what you mean by using the dot product and orthogonality to compute the length. is there a formula I'm missing?

Homework Statement Let L: R2 → Rn be a linear mapping. We call L a similarity if L stretches all vectors by the same factor. That is, for some δL, independent of v, |L(v)| = δL * |v| To check that |L(v)| = δL * |v| for all vectors v in principle involves an infinite number of...

i under the bound for the numerator, but i don't understand how to bound the denominator?

no i mean e times n. hence en or e*n.

the Euler number, e=2.718 or something i think. so en is e*n

Homework Statement Prove (n choose k) ≤ ((en)/k)^k by induction on k. Homework Equations I can't of anything that's awfully relevant besides the general steps of induction. The Attempt at a Solution So I found it true for the k=1 case which was easy enough. Then assumed true...

Ya I think I get it now. I was able to prove the basis. I'm doing the transformation now. Thanks for your help.

Homework Statement Let A be an 3x3 matrix so that A^3 = {3x3 zero matrix}. Assume there is a vector v with [A^2][v] ≠ {zero vector}. (a) Prove that B = {v; Av; [A^2]v} is a basis. (b) Let T be the linear transformation represented by A in the stan- dard basis. What is [T]B? Homework...