Recent content by charmmy

Homework Statement I have a question which asks me to find the dimensions of the subspace of even polynomials (i.e. polynomials with even exponents) and odd polynomials. I know that dim of Pn (polynomials with n degrees) is n+1. But how do I find the dimensions of even n odd polynomials...

Thanks.. But to make it a bit more easy to understand, do you by any chance have any example where we have to find a parametric representation of the intersection curve, instead of being able to compute it directly by substitutions of equations? That would be of a great help!

So, essentially, the boundaries of the radius is determined by whichever surface that has the smaller diameter? In this case, we use 0<r<2 (of the cylinder) instead of 0< r < 4 (of the hemisphere which has a bigger radius)?

Homework Statement Use the surface integral in stoke's theorem to calculate the circulation of the filed F around the curve C in the indicated direction: F= x2y3i + j+ zk C; the intersection of the cylinder x2+y2=4 and the hemisphere x2+y2+z2=16, z>=0, counterclockwise when viewed from above...

so is LaTeX Code: \\mathbf{\\nabla}\\left[f(x,y)g(x,y)\\right] = take h= f(x,y) g(x,y) then ∇h=dh/dx+dh/dy... What is the line integral of the gradient of a function over a closed curve? : is this just equal to zero? i'm quite confused

Homework Statement Let f(x,y) and g(x,y) be continuously differentiable real-valued functions in a region R. Show that ∫f ∇g · dr ]= − ∫g ∇f · dr for any closed curve C in R. Homework Equations The Attempt at a Solution I don't really know where to start, so I tried to evaluate...

the image would just be everything in R3 is that correct?

Okay. sorry about the confusion fzero: contraction does mean multiplication with a scalar between 0 and 1. dick: hmm in that case, x3 would be a free variable? since x2 and x1 must be zero.

I'ms so sorry about that. I didn't realize you've answered the question before I change it. Can I post both the questions under the same post then? 1. Homework Statement Q1) Show that a contraction transformation from V to V has a diagonal matrix representation regardless of the...

its only possible if x1 =0; x2=0 and x3=0 right? so its the trivial solution?

1. Homework Statement Q1) Show that a contraction transformation from V to V has a diagonal matrix representation regardless of the basis given to V (same basis in domain and range). !2) T(x1,x2,x3)=(x1,x2,x2*x3) find the kernel and range T for this transformation. 2. Homework Equations 3...

I have troubles arriving at the solution to this question: Consider the transformation T: P3-->P3 given by: T(f)=(1-x^2)f '' - 2xf ' Determine the bases for its range and kernel and nullity and rank Can anyone explain how should i go about finding the bases for its kernel and range?? i get 0...