Recent content by krozer

Homework Statement Find two complex polynomials f and g such that f(0)=f(-1)=1, f(1)=3 and g(x)=f(x-1) 2. The attempt at a solution Using Lagrange polynomial I got f such that f(0)=f(-1)=1, f(1)=3 Such f is defined by f(x)=x2+x+1 Now that...

Homework Statement Find two linear operators T and U on R^2 such that TU = 0 but UT ≠ 0. The Attempt at a Solution Let T(x1,x2)=(0,x2) Let U(x1,x2)=(x2,0) TU(x1,x2)=T(x2,0)=(0,0) Am I right? 'Cause I can't remember if TU(x1,x2)=T[U(x1,x2)] Or TU(x1,x2)=U[T(x1,x2)]

So I only proved it approaching by two rects, if I approach the limit by paraboloids, for example For y=x^2 \lim_{x \rightarrow 0} \dfrac{x^2sinx}{x}=\lim_{x \rightarrow 0} {xsinx}=0 Then I get two different values (the limit is 2 by the rects and is 0 by a paraboloid), so I don't know...

So If I put the limit as \lim_{x \rightarrow 0}\lim_{y \rightarrow 2} \dfrac{ysinx}{x}=\lim_{x \rightarrow 0}\dfrac{2sinx}{x}=2 Since \lim_{y \rightarrow 2} \dfrac{ysinx}{x}=\dfrac{2sinx}{x} Am I right?

Homework Statement \lim_{(x,y) \rightarrow (0,2)} \dfrac{ysinx}{x} The Attempt at a Solution I know that I have to evaluate the function in the given values of x and y For y=2 \lim_{x \rightarrow 0} \dfrac{2sinx}{x} Using L'Hopital \lim_{x \rightarrow 0} \dfrac{2cosx}{1}=2...

If I create a matrix whose columns are the vectors, and then I row-reduce it and there's a zero row, are the vectors lineraly dependent? why?

Does this have to do with the eigenvalues?

Ok, I think I know how to solve it.

Given that α,β,ɣ are linearly independent then, if we have that xα+yβ+zɣ=0 then x=y=z=0 Sup α+β=δ, β+γ=η and γ+α=ρ How do I prove δ ,η and ρ are linearly independent?. But answering your question I'm trying to prove it with the Ʃ(cδ)=0 for all c in R.

Thanks, proving (2) giving u is an element of Wm then u=(mx,x) x in R, now I know how to prove Wm is a subspace. Proving 3, you're right I forgot about the second coordinate.

Homework Statement Let F be a subset of the complex numbers. Let V be a vector space over F, and suppose α, β and γ are linearly independent vectors in V. Prove that (α+β), (β+γ) and (γ+α) are linearly independent. Homework Equations None. The Attempt at a Solution None. Thanks for your time.

I need help with this problem that I don't know how to solve. Homework Statement For each positive integer m, it's defined a subset of R2 as Wm={(mx,x)|x in R} (a) Prove that each Wm is a subspace of R2. (b) ¿Is the union of all Wm a subspace of R2?. Prove it. Homework Equations None. The...