(a) LT: PP, be the linear map defined by 71(p[:)) - 20)+p2 t), whores is the...
Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that is T(CO + C1x + c2x2) = co+C1(4x + 5) + c2(4x + 5)2. Find [7]3 with respect to the basis B = {1, x, x?}. Enter the second row of the matrix [7]z into the answer box below. i.e.. if A = [7]B. then enter the values a21, a22, 223, (in that order), separated with commas.
Problem #3: Let T: P2 P2 be the linear transformation defined by 7{p()) = (3x + 7) - that is 7(00+ cx + cox) = co + C (3x + 7) + C2(3x + 7)2 Find [7)with respect to the basis B = {1,x?). Enter the second row of the matrix 17 into the answer box below. i.e., if A = [718. then enter the values a1. 422, 223, (in that order), separated with commas. Problem #3:
Find the matrix [T], p of the linear transformation T: V - W with respect to the bases B and C of V and W, respectively. T:P, → P, defined by T(a + bx) = b - ax, B = {1 + x, 1 – x}, C = {1, x}, v = p(x) = 4 + 2x [T] C+B = Verify the theorem below for the vector v by computing T(v) directly and using the theorem. Let V and W...
: 2: Let T : P1 → P2 be the linear map taking a polynomial p(t) to its antiderivative P(t) satisfying P(0) = 0 (e.g. T(5 + 2t) 5t + t2). Find two matrices A, B representing the corresponding linear map R2 + R3, the first with respect to the standard bases of P2 and P3, and the second with respect to the bases B = {1,1+t} B' = {1,1 +t, 1+t+t2}
Let T be a linear map from R3[z] to R2[z] defined as (T p)(z) = p'(z). Find the matrix of T in the basis: 4 points] Let T be a linear map from Rals] to R12] defined as (TP)(z) = p,(z). Find the matrix of T in the basis: in R2[-]; ~ _ s, r2(z) (z-s)2 in R2 [2], where t and 8 are real numbers. T1(2 Find coordinates of Tp in the basis lo, 1, 12 (if p is...
(1 point) Let f:R → R'be the linear transformation defined by T 4 -5 51 f(T) = -1 2 - 5 . | -4 0 3 Let B = {(-2,-1, 1), (-2, -2,1),(-1,-1,0)}, C = {{-2, -1, 1), (2,0, -1),(-1,1,0)}, be two different bases for R3. Find the matrix f for f relative to the basis B in the domain and C in the codomain. IT 3
(1 point) How many different functions f : S + T can be defined that map the domain S = {1,2,3,...,6} to the range T = {1,2,3,..., 15) such that f is NOT one-to-one? Enter your answer in the box below. Answer =
6. Let T:P, P, be the linear operator defined as (p(x)) = p(5x), and let B = {1,x,x?} be the standard basis for Pz. a.) (5 points) Find [T]s, the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x?. Determine [p(x)]s, then find T(p(x)) using [T]g from part a. c.) (1 point) Check your answer to part b by evaluating T(x+6x²) directly.
5. Let T: P2 Dasis for P2. P2 be the linear operator defined as T(P(x)) = p(5x), and let B = {1,x, x2} be the standard Find [T]b, the matrix for T relative to B. Let p(x) = x + 6x2. Determine [p(x)]B, then find T(p(x)) using [T]s from part a. Check your answer to part b by evaluating T(x + 6x2) directly.
Suppose T: M2,2 P2 is a linear transformation whose action is defined by s and that we have the ordered bases 1 00 1 0 000 0 00 010 0 1 D-1x2 for M2.2 and P2 respectively. a) Find the matrix of T corresponding to the ordered bases B and D MD(T) 0 0 0 b) Use this matrix to determine whether T is one-to-one or onto < Select an answer >, < Select an answer >