Problem #3: Let T: P2 P2 be the linear transformation defined by 7{p()) = (3x +...
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.
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
2. Let T be the linear transformation from P2 to R2 defined by 20 – 201 T(@o+at+aat) = | 0o + a1 + a2 Find a basis for the range of T.
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
(a) LT: PP, be the linear map defined by 71(p[:)) - 20)+p2 t), whores is the set of all polynomials in over the real numbers of degree or less Suppose that is the matrix of the transformation T:P, P, with respect to standard bases S, - 1,t) for the domain and S, - {1, 2} for the cododman. Find the matrix and enter your answer in the box below. na 52 b) In the following commutative diagram, A P, Po...
Let T: P2 + P, be a linear transformation for which T(1) = 3 - 2x, 7(x) = 9x – x2, and 7(x2) = 2 + 2x2. Find T(2 + x - 8x?) and T(a + bx + cx?). T(2 + x - 8x2) T(a + bx + cx) II
let T: P2 --> R be the linear transformation defined by T(p(x))=p(2) a) What is the rank of T? b)what is the nullity of T? c)find a basis for Ker(T)
Problem 11. Let M2 → P3 be the linear transformation defined by: ((? 2)) -the top te B=(69) C3):69):69)) Taking the basis: of M, and the basis: C = (1, 24, 322, 4.c.) of P3, [flB.c is: 1. /1 0 0 0 0 2 0 0 0 0 3 0 10 0 0 4) 2. /1 0 0 0 10 0 0 0 0 0 0 0 0 1 (0 0 0 10 o 14 0 0 0 (1 700...
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 >
Let T: P1 → P2 be a linear transformation defined by T(a + bx) = 3a – 2bx + (a + b)x². (a) Find range(T) and give a basis for range(T). (b) Find ker(T) and give a basis for ker(T). (c) By justifying your answer determine whether T is onto. (d) By justifying your answer determine whether T is one-to-one. (e) Find [T(7 + x)]], where B = {-1, -2x, 4x2}.