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:
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:
Define T: P2 ? P2 by Tao + ax + a2x2) = (-3a1 + 5a2) + (-4a0 + 4a1-10a2)x + 4a2x2 Find the eigenvalues. (Enter your answers from smallest to largest.) a1, A2, A3) = | |-2.4.6 Find the corresponding coordinate eigenvectors of T relative to the standard basis f1, x, x2 ?,0,1) X2 =?-5,1
Define T: P2 → P2 by T(ao + a1x + a2x2) = (-3a1 + 5a2) + (-420 + 421 – 10a2)x + 5a2x2. Find the eigenvalues. (Enter your answers from smallest to largest.) (11, 12, 13) = ( –2,5,6 ) Find the corresponding coordinate eigenvectors of T relative to the standard basis {1, x, x2}. x1 = -5,10,0 X2 = *3 = -2,1,0
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 T: P2 → P2 be defined by T(p(x)) p(7x + 8) (a) Find the determinant of T. (b) Find the eigenvalues of T. :
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.
Let T. M2(R) →P2(R) be defined by T.(Iga)-(+b) + (b+c) Let T2: P2 (R) → Pl (R) be defined by Tap(x))-p' (x) (c+ d)x2 2. Find Ker(T2 . T) and find a basis for Ker(T2。T).
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.
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: