Let T:P2 → p2 be defined by T(p(x)) = p(6x + 7) (a) Find the determinant...
Let T: P2 → P2 be defined by T(p(x)) p(7x + 8) (a) Find the determinant of T. (b) Find the eigenvalues of T. :
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 #6: Let T:p2 → p2 be defined by T(ao +ajx + a2 x2) = (890 +6a1 + 902) – (a1 + 36a2)x + (20 – 4a2) x2 + Find the eigenvalues of T. Enter any repeated eigenvalues as often as they repeat. Problem #6: Just Save Submit Problem #6 for Grading Problem #6 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark:
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.
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:
6. Let T: P2P be the linear operator defined as T(p(x)) = P(5x), and let B = {1,x,x?} be the standard basis for P2 a.) (5 points) Find [T), the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x2 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 + 6x) directly
6. Let :P - P be the linear operator defined as (p(x)) - (5x), and let B = (1.x.x) be the standard basis for P2 a.) (5 points) Find the matrix for T relative to B. b.) (4 points) Let p(x) = x + 6x Determine (px)then find (p(x)) using (Tle from parta c.) (1 point) Check your answer to part b by evaluating T(x+6x) directly
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 #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:
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: