Problem #6: Let T:p2 → p2 be defined by T(ao +ajx + a2 x2) = (890...
Problem #6: Let T:p2 → 2 be defined by T(ao +ajx + a2 x2) = (7a0 + a1 - 7a2) - (a1 + 25a2)x+ 20 x2 Find the eigenvalues of T. Enter any repeated eigenvalues as often as they repeat. Problem #6: Just Save Submit Problem #6 for Grading Attempt #1 Attempt #2 Attempt #3 Problem #6 Your Answer: Your Mark:
1 #6: Let T: P2 → p2 be defined by T(ao +ajx + a2 x2) = (Tao + 381 +8a2) – (a1 + 36a2)x+ 20 x2 Find the eigenvalues of T. Enter any repeated eigenvalues as often as they repeat. em #6:
Let T:P2 → p2 be defined by T(p(x)) = p(6x + 7) (a) Find the determinant of T. (b) Find the eigenvalues of T.
Only part C please.
Problem #1: Let T: P2 → P3 be the linear transformation defined by T{p(x)) = xp(x). (a) Find the matrix for T relative to the bases B = {ui, U2, U3} and B' = {V1, V2, V3, V4}, where uj = 8, u2 = x, u3 = x2 + 5x, v1 = 1, v2 = x, V3 = x2, 14 = x3. (b) Let x = 16 + 4x + 9x2. Find [x]B. (c) Let x...
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y Find Y(s), the Laplace transform ofy() Enter your answer as a symbolic function of s, as in these examples Problem #2: Submit Problem #2 for Grading Just Save Attempt #3 Problem #2 Attempt # 2 Attempt #5 Attempt#1 Attempt #4 Your Answer: Your Mark
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:
QUESTION 4 Let T R3-P2 be defined by T(a, b, c) - (a + b + e) +(a+b)a2 (4.1) Show that T is a linear transformation (4.2) Fınd the matrix representation [T]s, B, of T relative to the basıs in R3 and the basis in P2, ordered from left to right Determine the range R(T of T Is T onto? In other words, is it true that R(T)P2 Let x, y E R3 Show that x-y ker(T) f and only...
Problem #6: Consider the following integral equation, so called integral because the unknown dependent variable y appears within an This equation is defined for t0 (a) Use convolution and Laplace transforms to find the Laplace transform of the solution (b) Obtain the solution y(t) Enter your answer as a symbolic function of s, as in these examples Problem #6(a): Enter your answer as a symbolic function of t, as in these examples Problem #6(b): Just Save Submit Problem #6 for...
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)]B, where B={−1,−2x,4x2} Please solve it in very detail, and make sure it is correct.
Let T:P1→P2T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2.T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T)range(T) and give a basis for range(T)range(T). (b) Find ker(T)ker(T) and give a basis for ker(T)ker(T). (c) By justifying your answer determine whether TT is onto. (d) By justifying your answer determine whether TT is one-to-one. (e) Find [T(7+x)]B[T(7+x)]B, where B={−1,−2x,4x2}B={−1,−2x,4x2}.