Recent content by Cassi

Thank you, this was very helpeful. So I see that when it is a polynomial, I know repeat this with b1 = x, etc.

I did not abandon a thread. I asked a new question for clarification. How do you calculate the projection of a particular function? Thank you for your insightful help.

I do not see the relationship between the definition of a projection and finding the specific projection of a function. I do not understand how to apply the concept.

Homework Statement In the real linear space C(-1, 1) with inner product (f, g) = integral(-1 to 1)[f(x)g(x)]dx, let f(x) = ex and find the linear polynomial g nearest to f. Homework EquationsThe Attempt at a Solution I understand that the best approximation for g is equal to the projection of...

This is the abbreviated formula given to me in my book from the more complex Gram-Schmidt formula. Maybe I will try using the original formulas.

Homework Statement In the real linear space C(1, e), define an inner product by the equation (f,g) = integral(1 to e)(logx)f(g)g(x)dx. (a) If f(x)=sqrt(x), compute ll f ll (the norm of f) (b) Find a linear polynomial g(x)=a+bx that is orthagonal to the constant function f(x)=1 Homework...

Homework Statement Let V consist of all infinite sequences {xn} of real numbers for which the series summation xn2 converges. If x = {xn} and y = {yn} are two elements of V, define (x,y) = summation (n=1 to infinity) xnyn. Prove that this series converges absolutely. Homework Equations The...

Homework Statement In the linear space of all real polynomials with inner product (x, y) = integral (0 to 1)(x(t)y(t))dt, let xn(t) = tn for n = 0, 1, 2,... Prove that the functions y0(t) = 1, y1(t) = sqrt(3)(2t-1), and y2 = sqrt(5)(6t2-6t+1) form an orthonormal set spanning the same subspace...

Homework Statement In the real linear space C(1, 3) with inner product (f, g) = intergal (1 to 3) (f(x)g(x))dx, let f(x) = 1/x. Knowing that g = (1/2)log3 is the constant polynomial g that is nearest to f. Compute llg-fll2 for this g. Homework EquationsThe Attempt at a Solution I devised...

Homework Statement In the real linear space C(1, 3) with inner product (f,g) = integral (1 to 3) f(x)g(x)dx, let f(x) = 1/x and show that the constant polynomial g nearest to f is g = (1/2)log3. Homework EquationsThe Attempt at a Solution I seem to be able to get g = log 3 but I do not know...

Homework Statement Find an orthonormal basis for the subspace of V4 spanned by the given vectors. x1 = (1, 1, 0, 1) x2 = (1, 0, 2, 1) x3 = (1, 2, -2, 1) Homework Equations Gram-Schmidt Process The Attempt at a Solution I have used the Gram-Schmidt process but seem to be running into trouble...

Homework Statement A curve has the equation y2 = x3. Find the length of the arc joining (1, - 1) to (1, 1). Homework Equations The Attempt at a Solution I took the integral of the distance and tried to evaluate from -1 to 1. L = [intergral (-1 to 1) sqrt (1+(dy/dx x^3/23/2)2 dx] Evaluated I...

Homework Statement For the real-valued function All f with 2f(0)=f(1) with domain [0, 1], determine whether the given set is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. Homework...

Thank you, this helps. I knew what the conclusion needed to be but had a hard time phrasing it. Thank you!

So would I say, let f and g be in S such that they satisfy the given condition. Now f+g exist in S because f(0)+g(0)=f(1)+g(1) therefore the first axiom stands. And for the second cf exists in S because cf(0)=cf(1), therefore the second axiom stands. Is this a valid argument?