Recent content by Technique101

Hmm, I don't know if I quite follow. So: D(1,0,0) = 2x = (0,2,0) D(0,1,0) = 1 = (0,0,1) D(0,0,1) = 0 = (0,0,0) So what would be the next step?

Homework Statement Find the matrix of the linear operator with respect to the given basis B. D: P2 -> P2 defined by D(ax2 + bx + c) = 2ax+b, B = { 3x2+2x+1, x2-2x, x2+x+1 }Homework Equations None. The Attempt at a Solution I set the basis B = { (3,2,1), (1,-2,0), (1,1,1) } based on the...

Okay, thanks guys! I just sort of needed a kick-start to get going. I figured it out, so thanks again!

Says to prove that V is a vector space over R

Okay, so i state that since b1 > 0 and b2 > 0, therefore b1*b2 > 0, and therefore is closed under addition and therefore is in the set. I do the same for scalar multiplication. For a question like this, do I really need to prove all 10 axioms, or is there a more simplified way to prove...

Hey guys, new to the forum here, and its midterm time and I am working through a few questions and I can't seem to figure this one out. Homework Statement Let S = { (a,b) | b > 0 } and define addition by (a,b) + (c,d) = (a*d + a*c, b*d) and define scalar multiplication by k(a,b) = (...