Question

Suppose T: P2(R) ---> P2(R) by T(p(x)) = x^2 p''(x) + xp'(x) and U : P2(R)...

Suppose T: P2(R) ---> P2(R) by T(p(x)) = x^2 p''(x) + xp'(x) and U : P2(R) --> R by U(p(x)) = p(0) + p'(0) + p''(0).

a. Calculate U composed of T(p(x)) without using matricies.

b. Assuming the standard bases for P2(R) and R find matrix representations of T, U, and U composed of T.

c. Show through matrix multiplication that the matrix representation of U composed of T equals the product of the matrix representations of U and T.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let T : P(R) → P(R) be the linear map defined by T(p(x)) = xp′(x) (you...
Let T : P(R) → P(R) be the linear map defined by T(p(x)) = xp′(x) (you may take it for granted that T is linear). Show that for each λ ∈ Z with λ ≥ 0, λ is an eigenvalue of T , and xλ is a corresponding eigenvector.
Consider the vector space P2 := P2(F) and its standard basis α = {1,x,x^2}. 1Prove that...
Consider the vector space P2 := P2(F) and its standard basis α = {1,x,x^2}. 1Prove that β = {x−1,x^2 −x,x^2 + x} is also a basis of P2 2Given the map T : P2 → P2 defined by T(a + bx + cx2) = (a + b + c) + (a + 2b + c)x + (b + c)x2 compute [T]βα. 3 Is T invertible? Why 4 Suppose the linear map U : P2 → P2 has the matrix representation...
a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3...
a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3 as T( →u ) = T(x, y, z) = (x + y, 2z − y, x − z) Find the standard matrix for T and decide whether the map T is invertible. If yes then find the inverse transformation, if no, then explain why. b. Let (x, y, z) ∈ R^3 be given T : R^3 → R^2 by T(x, y, z) = (x...
1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y,...
1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y, 5x + y). (a) Represent T as a matrix with respect to the standard basis for R 2 . (b) First, show that B = {(1, 1),(−2, 5)} is another basis for R 2 . Then, represent T as a matrix with respect to B. (c) Using either (a) or (b), find the kernel of T. (d) Is T an isomorphism? Justify your answer....
Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that satisfy the first-order system...
Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that satisfy the first-order system of PDE Ut=Vx, Vt=Ux, A.) Show that both U and V are classical solutions to the wave equations  Utt= Uxx. Which result from multivariable calculus do you need to justify the conclusion. B)Given a classical sol. u(t,x) to the wave equation, can you construct a function v(t,x) such that u(t,x), v(t,x) form of sol. to the first order system.
2.23. Let R be a commutative ring. Suppose that P is a subset of R with...
2.23. Let R be a commutative ring. Suppose that P is a subset of R with the following properties: P1: For any element a ∈ R, one and only one of the following holds: a = 0, a ∈ P, or −a ∈ P. P2: P is closed under addition and multiplication. Define an order relation < on R by saying that for a, b ∈ R, a < b if b − a ∈ P. Show that < satisfies...
A random variable XX with distribution Exponential(λ)Exponential(λ) has the memory-less property, i.e., P(X>r+t|X>r)=P(X>t) for all r≥0...
A random variable XX with distribution Exponential(λ)Exponential(λ) has the memory-less property, i.e., P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0.P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0. A postal clerk spends with his or her customer has an exponential distribution with a mean of 3 min3 min. Suppose a customer has spent 2.5 min2.5 min with a postal clerk. What is the probability that he or she will spend at least an additional 2 min2 min with the postal clerk?
Consider V = fp(t) 2 P2 : p0(1) = p(0)g, where P2 is a set of...
Consider V = fp(t) 2 P2 : p0(1) = p(0)g, where P2 is a set of all polynomials of degree less than or equal to 2. (1) Show that V is a subspace of P2 (2) Find a basis of V and the dimension of V
1. Let p be any prime number. Let r be any integer such that 0 <...
1. Let p be any prime number. Let r be any integer such that 0 < r < p−1. Show that there exists a number q such that rq = 1(mod p) 2. Let p1 and p2 be two distinct prime numbers. Let r1 and r2 be such that 0 < r1 < p1 and 0 < r2 < p2. Show that there exists a number x such that x = r1(mod p1)andx = r2(mod p2). 8. Suppose we roll...
The problem is to maximise utility u(x, y) =2*x +y s.t. x,y ≥ 0 and p*x...
The problem is to maximise utility u(x, y) =2*x +y s.t. x,y ≥ 0 and p*x + q*y ≤ w, where p=13.4 and q=3.9 and w=1. Here, * denotes multiplication, / division, + addition, - subtraction. The solution to this problem is denoted (x_0, y_0) =(x(p, q, w), y(p, q, w)). The solution is the global max. Find ∂u(x_0,y_0)/∂p evaluated at the parameters (p, q, w) =(13.4, 3.9, 1). Write the answer as a number in decimal notation with at...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT