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3. Let T:RE → Rž be a linear transformation, given my the formula [2x1 +3.27 T(Xje1...
10. (10 pt) Let bi1 The set B tbi,b2) is a basis for R2. Let T : R2 →R2 is a linear transformation such that T(bi) 7bi +7b2 and T (b2) 3bi +4b2 Then the matrix of T relative to the basis B is and b2- -1 4 [T]B and the matrix of T,relative to the standard basis E for R2 is
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
6. Let T P2 P be a linear transformation such that T P2P2 is still a linear trans formation such that T(1) 2r22 T(2-)=2 T(1) = 2r22 T(12 - )=2 T(x2x= 2r T(r2)2x (a) (6 points) Find the matrix for T in some basis B. Specify the basis that you use. (d) (4 points) Find a basis for the eigenspace E2. (b) (2 points) Find det(T) and tr(T') (e) (4 points) Find a basis = (f,9,h) for P2 such that...
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=
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
Let B = {b1,b2, b3} be a basis for a vector space V. Let T be a linear transformation from V to V whose matrix relative to B is [ 1 -1 0 1 [T]B = 2 -2 -1 . 10 -1 -3 1 Find T(-3b1 – b2 - b3) in terms of bı, b2, b3 .
Find the matrix of the linear transformation T: V →W relative to B and C. Suppose B = {bı, b2, b3} is a basis for V and C = {C1, C2} is a basis for W. Let T be defined by T(b]) = 261 + C2 T(62) = -501 +502 T(b3) = 2C1-802 2. 3 0 2 -6 [3 0 -6 1 5-8 2 -5 2 5 -8 2 1 -5 5 2 -8
show work pls! Let L :P2 →P3 be the linear transformation given by L(p(t)) = 5p"(t) + 3p' (t) + 1p(t) + 4tp(t). Let E = (e1, C2, C3) be the basis of Pề given by ei(t) = 1, ez(t) = t, ez(t) = 62. and let F = (f1, f2, f3, f4) be the basis of P given by fi(t) = 1, fz(t) = t, f3(t) = ť, fa(t) = {'. Find the coordinate matrix LFE of L relative...
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.