B is the matrix of T: V → V with respect to a basis H, and...

Question

Question

Answer 1

Answer #1

Let u be a F.D.V.S. over the field F arod let Gard H are ordered basis for V. Suppose Tivv is linear operator. If P=CP, – an]

Answer 2

Similar Homework Help Questions

Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x,...

Find the matrix A' for T relative to the basis B'. T: R2 + R2, T(x, y) = (3x - y, 4x), B' = {(-2, 1), (-1, 1)} A' = Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let 0 2 A = 3 4 be the matrix for T: R2 + R2 relative to B. (a) Find the transition matrix P from B' to B. 6 4 P= 9 4...
Detailed steps please ->R3 be defined by natural basis of R and let T 1,0,1), (0,1.1).(0,0,1))...

Detailed steps please ->R3 be defined by natural basis of R and let T 1,0,1), (0,1.1).(0,0,1)) be another basis for R. Find the matrix representing L with respect to a) S. b) S and T d) T e) Find the transition matrix Ps from T- basis to S- basis. f) Find the transition matrix Qr-s from S-basis to T-basis. g) Verify Q is inverse of P by QP PQ I. h) Verify PAP-A
know how to find the matrix representation [T]5 for a linear transforma- tion T V W...

know how to find the matrix representation [T]5 for a linear transforma- tion T V W with respect to bases a, B for V, W, respectively. know how to use the matrix representation [T5 and the coordinate map- pings R of T W to find bases for the kernel and image V, :Rm -> given two bases a, from a coordinates to 3 coordinates for Rn, know how to find the change of basis matrix know how to find the...

{(1,3), (2,-2)} and B = {(-12,0), (-4, 4)} be the basis for R2 and let A...

{(1,3), (2,-2)} and B = {(-12,0), (-4, 4)} be the basis for R2 and let A = 7. Let B 3 2 0 4 be the matrix for T R2 -> R2 relative to B (a) Find the transition matrix P from B' to B (b) Use the matrices A and P to find [v]B and [T(v)]B where v] 2 (c) Find P and A' (the transition matrix for T relative to B') (d) Find [T(v)B' in two ways: first...
Find the matrix [T] C-B of the linear transformation T: VW with respect to the bases...

Find the matrix [T] C-B of the linear transformation T: VW with respect to the bases B and C of V and w, respectively. T: R2 + R3 defined by a + 2b -a b +[:] s={{ ;][-:} c-{{0}{} --13) [) CBT
To enter a basis to WeWork, place the entries of each vector inside of brackets and...

To enter a basis to WeWork, place the entries of each vector inside of brackets and enter a list of these vectors, separated Note: You can eam partial credit on this problem Problem 7. (9 points) Let E be the standard basis in Rand let B be an ordered basis in R (a) Find the transition matrix T from the basis to the basis B (b) Find the coordinates of the vector v with respect to the ordered basis B...

Find the matrix [T], p of the linear transformation T: V - W with respect to...

Find the matrix [T], p of the linear transformation T: V - W with respect to the bases B and C of V and W, respectively. T:P, → P, defined by T(a + bx) = b - ax, B = {1 + x, 1 – x}, C = {1, x}, v = p(x) = 4 + 2x [T] C+B = Verify the theorem below for the vector v by computing T(v) directly and using the theorem. Let V and W...
1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be...

1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be the natural basis of R2 and let T = {(-1,2), (2,0)) be another basis for R2 . Find the matrix representing L with respect to a) S b) S and1T c) T and S d) T e) Find the transition matrix Ps- from T basis to S basis. f) Find the transition matrix Qre-s from S-basis to T-basis. g) Verify Q is inverse of...
Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B...

Exercise 1. Let S(2) = (€1,6) be the standard basis of T R2 and let B = (? =-3e1 + 2e, v2 = 2e1-6). Show that B is a basis of T. Now suppose that a linear mapping f : T T is represented with respect to 8(2) by the matrix oSe 4 6' Find the matrix B that represents f with respect to B.

4, =(7,5), u =(-3,-1) 2) Let v = (1,-5), v = (-2,2) and let L be...

4, =(7,5), u =(-3,-1) 2) Let v = (1,-5), v = (-2,2) and let L be a linear operator on Rwhose matrix representation with respect to the ordered basis {u,,,) is A (3 -1 a) Determine the transition matrix (change of basis matrix) from {v, V, } to {u}. (Draw the commutative triangle). b) Find the matrix representation B, of L with respect to {v} by USING the similarity relation