Let T: P2 → P2 be defined by T(p(x)) p(7x + 8) (a) Find the determinant...
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.
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: 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)
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. 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).
3. Let T : P2(R) → P2(R) be defined by T(f(x)) = f'(x). Find an element v ∈ P2(R) such that v, T v, T^2 v is a basis of generalized eigenvectors 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.
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
8. Let L: P2 → P be the linear transformation defined by Lar? +bt + c) = (a + b)t +(b - c). (a) Find a basis for ker L. (b) Find a basis for range L.
Let V P2(R) and let T V-V be a linear transformation defined by T(p)-q, where (x)(r p (r Let B = {x, 1 + x2, 2x-1} be a basis of V. Compute [TIB,B, and deduce if it is eigenvectors basis of