Recent content by jeffreylze

How did you get that? Can you bring me through the steps?

Homework Statement http://img132.imageshack.us/img132/6663/captureqqi.jpg Homework Equations The Attempt at a Solution I came up with this answer and i don't know how to continue: (1+1/n)^n I understand I have to put in limit n -> infinty. But can i put the limit inside the...

I am such a douche + a slow learner =/ Yeah, i get it (x+2) in P2 is (2,1,0) (it is just the same thing like the previous example! careless me) x in p1 is just (0,1) so (x^2+2x) in P2 will be (0,2,1). So the matrix will be A = (2,1,0 ; 0,2,1) So a different basis will still be the same. Say B...

Using that method, i tried solving this question but to no avail : Find the matrix representation of T:P1 > P2 with respect to bases B = {1,x} and C {1,x,x2} where T(p) = (x+2)p for p\inP1 p = a0 + a1x T(1) = (x+2) T(x) = (x2+2x) and I don't know how to map that to P2

Oh, so p(x) = x , x in p2 will map it to x2 in p3? - (0,0,1,0) p(x) = x2, X2 in p2 will map it to x3 in p3 - (0,0,0,1) So that gives me A = [0 0 0; 1 0 0 0 1 0; 0 0 1] ? But is there a faster way to do this? I came across this equation while looking...

I don't really understand this part, how does 1 in p2 maps to x in p3 ?

Homework Statement Let T: P2 > P3 denote the function defined by multiplication by x :T(p(x)) = xp(x). In other words, T(a+bx+cx2) = ax+bx2+cx3 (a) Show that T is a linear transformation. (b) Find the matrix of T with respect to the standard bases {1,x,x2} for P2 and {1,x,x2,x3} for P3...

The product should give me a zero vector. What about for the image, question 39 ?

Homework Statement 38) Determine whether or not v1 = (-2,0,0,2) and v2 = (-2,2,2,0) are in the kernel of the linear transformation T:R^4 > R^3 given by T(x) = Ax where A = [1 2 -1 1; 1 0 1 1; 2 -4 6 2] 39) Determine whether or not w1 = (1,3,1) or w2 = (-1,-1,-2) is in...

But what i did for part(a) is right?

fantastic, at least now I know I am making some progress. =D

Homework Statement determine whether or not the given set is a basis for C^3 ( as a C-vector space) (a) {(i,0,-1),(1,1,1),(0,-i,i)} (b) {(i,1,0),(0,0,1)} Homework Equations The Attempt at a Solution All I did was to put the 3 vectors in part (a) into a matrix as 3 columns...

Homework Statement Let H and K be subspaces of a vector space V. Prove that the intersection K\cap H is a subspace of V. Homework Equations The Attempt at a Solution This, I have absolutely NO idea how and where to start. Are there any axioms which can be used to prove this?

Actually only V1 and V2 forms a basis, as v3 can be written as a linear combination of V1 and V2. C1*(1,-1,2) + C2*(0,1,1) = (1,1,1) . I formed a matrix A with (1,-1,2) and (0,1,1) in columns and then put (1,1,1) into the matrix in augmented form. But the system is inconsistent, no solutions...

Okay, thanks. Now that make sense =D