By justifying your answer, determine whether the function T is a linear transformation. (a) T :...
Determine whether or not the following transformation T :V + W is a linear transformation. If T is not a linear transformation, provide a counter example. If it is, then: (i) find the nullspace N(T) and nullity of T, (ii) find the range R(T) and rank of T, (iii) determine if T is one-to-one, (iv) determine if T is onto. : (a) T: R3 + R2 defined by T(x, y, z) = (2x, y, z) (b) T: R2 + R2...
answer, determine whether the function linear transformation T: R² M₂,2 define as TG y z)=Rz xty Loc-32 x-y ST: P - R defined as I (at boct (x²) = a-2b +36
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}.
linear algebra Determine whether the function is a linear transformation. T: R2 R3, T(x, y) = (x,xy, vy) O linear transformation O not a linear transformation
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}.
Determine whether the function is a linear transformation. T: R2 R3, T(x,y) = (Vx, 5xy, vy) O linear transformation not a linear transformation
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...
Let V be a vector space and W be a subset of V. By justifying your answer, determine whether W is a subspace of V. (a) V = M2,2 and EV : ad = bc (b) V = P3 and W = {a + bx + cx? + dx€ V: a+c= b+d}. +
a bans for range (T) Let TPP, le a linear transformation defned by T (a + bx) = 3a - 2 boct Carb) (b) Find Ker (G) and give a basis for Ker (T) (c) By justifying your answer determine wheller (d) By justifying your answer determine whether Find [T(7 + x)] where B= 2-1, -2x, Axe" xx"}