For cach problenm . Show T:V→V is linear Find the matrix of T in tne standard bosis Find the ker Find the matrix of Tina non-standard basis 1·V-R, T rotates each XEv countt r cock wise by nci and...
1. For each of the following linear operators T:V + V, find the Jordan canonical form together with a Find the Jordan canonical basis B for V. Feel free to use a Wolfram Alpha or whatever to calculate the characteristic polynomial, but you should complete the rest of the question without computer assistance (i.e., show your steps). (a) The map T : R4 → R4 given by T(v) = Av where -3 1 27 _ A=1 -2 1 -1 2||...
Consider the linear transformation T: "R" whose matrix A relative to the standard basis is given. A=[1:2] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12) = 2,3 |_) (b) Find a basis for each of the corresponding eigenspaces. B = X B2 = = {I (c) Find the matrix A' for T relative to the basis B', where B'is made up of the basis vectors found in part (b). A=
show all parts and explain
- For each linear transformation f :V W, find the associated matrix. W with given bases for V and (a) tr : M22 → R (trace of a matrix) with R-basis {1} and M22-basis (19):( :) :( 9):( )} (b) E: P2 → R2 which sends f e P, to [f( 1), f(2)] € R2, and the standard bases. (c) Given some basis B = {81,...,Bn} of V, the linear transforma- tion C: V →...
Consider a linear space P2(R) with the standard basis S- {1,t,t, t 3). a. Describe the isomorphism P R sending p(t) ps b. Show that B [t - 1,t + 1,t2 +t, t3) is another basis for P3 (R). c. Let p(t) 32t4t3. Find p. d. Show that the map P R4 sending p(t)-, рв is an isomorphism.
(Note: Each problem is worth 10 points). 1. Find the standard matrix for the linear transformation T: that first reflects points through the horizontal L-axis and then reflects points - through the vertical y-axis. 2. Show that the linear transformation T: R - R whose standard [ 2011 matrix is A= is onto but not one-to-one. - R$ whose standard 3. Show that the linear transformation T: R 0 1 matrix is A = 1 1 lov Lool is one-to-one...
For each transformation below, find the value of T(U). 1) Let T be a linear transformation from R$ to M2 (R) 2 Let B= -1 2 3 Let C= [1].[133] [131] 1 -22 -21 -22 -21 -59 14 13 Let M= be the matrix transformation of T from basis B to C 37 -59 30 30 -19 -1 Let v= 2 2 The value of T(0) = 2) Let T be a linear transformation from P3 (R) to M22(R). Let...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...