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\ A =1 6 2 1) and T : Rº → R such that matriz A is the -3 0 7 1 transformation matriz in relation to bases B and B' a) Find a formula and a basis for T(1.r2, 13, 74) and use this formula to get T(2,2,0,00) 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\ A =1 6 2 1) and T : Rº → R such that matriz A is the -3 0 7 1 transformation matriz in relation to bases B and B' a) Find a formula and a basis for T(1.r2, 13, 74) and use this formula to get T(2,2,0,00) b Find Im(T) and a basi for the Im(T).What is the dim(Im(T))
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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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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