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Given B = v1 {(0, 1, 1, 1)} , v2 = {2, 1, – 1, –1}, v3 {(1,4, –1, 2)} , v4{(6,9, 4, 2)} B' = wi {(0, 8, 8)} , wz = {-7,8, 1} , ws {(-6,9, 1)} 3 -2 1 0\ 1 6 2 1 -3 0 7 1, transformation matrix in relation to bases B and B' %3D %3D A = and T : Rª → R such that matrix A is the a) Find a formula and a basis for T('1.r2, x3, x4) and use this formula to get T(2,2,0, 0) b Find Im(T) and a basi for the Im(T).What is the dim(Im(T))

Given B = v1 {(0, 1, 1, 1)} , v2 = {2, 1, – 1, –1}, v3 {(1,4, –1, 2)} , v4{(6,9, 4, 2)} B' = wi {(0, 8, 8)} , wz = {-7,8, 1} , ws {(-6,9, 1)} 3 -2 1 0\ 1 6 2 1 -3 0 7 1, transformation matrix in relation to bases B and B' %3D %3D A = and T : Rª → R such that matrix A is the a) Find a formula and a basis for T('1.r2, x3, x4) and use this formula to get T(2,2,0, 0) b Find Im(T) and a basi for the Im(T).What is the dim(Im(T))

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Linear Algebra Given B = v1 {(0, 1, 1, 1)} , v2 = {2, 1, – 1, –1}, v3 {(1,4, –1,2)} , v4{(6,9, 4, 2)} B' = wi {(0, 8, 8)} , w2 = {-7,8, 1} , w3 {(-6,9, 1)} 3 -2 1 0V A =| 1 6 2 1 -3 0 7 1) transformation matrix in relation to bases B and B' and T : R → R such that matria A is the a) Find a formula and a basis for T('1.r2, 13, z4) and use this formula to get T(2,2,0,0) b Find Im(T) and a basi for the Im(T).What is the dim(Im(T))
Transcribed Image Text:Linear Algebra Given B = v1 {(0, 1, 1, 1)} , v2 = {2, 1, – 1, –1}, v3 {(1,4, –1,2)} , v4{(6,9, 4, 2)} B' = wi {(0, 8, 8)} , w2 = {-7,8, 1} , w3 {(-6,9, 1)} 3 -2 1 0V A =| 1 6 2 1 -3 0 7 1) transformation matrix in relation to bases B and B' and T : R → R such that matria A is the a) Find a formula and a basis for T('1.r2, 13, z4) and use this formula to get T(2,2,0,0) b Find Im(T) and a basi for the Im(T).What is the dim(Im(T))
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