2. Let L: R4 R3 be defined by L ([u₁ u2 uz u4]) = [u₁ u₂+ Uz Uz + U₁] Let S and T be the natural bases for R4 and R3, respectively. Let S' = {[1 0 0 0 1], [0 0 0 1],[1 1 0 0], [0 1 1 0]} and T' = {[1 1 0], [0 1 0], [ 1 0 1]} (a) Find the representation of L with respect to S and T. (b) Find the representation of L with respect to S' and T'. (c) Find L([2 1 -1 3]) by using the matrices obtained in parts (a) and (b) and compare this answer with that obtained from the definition for L.
2. Let L: R4 R3 be defined by L ([u₁ u2 uz u4]) = [u₁ u₂+ Uz Uz + U₁] Let S and T be the natural bases for R4 and R3, respectively. Let S' = {[1 0 0 0 1], [0 0 0 1],[1 1 0 0], [0 1 1 0]} and T' = {[1 1 0], [0 1 0], [ 1 0 1]} (a) Find the representation of L with respect to S and T. (b) Find the representation of L with respect to S' and T'. (c) Find L([2 1 -1 3]) by using the matrices obtained in parts (a) and (b) and compare this answer with that obtained from the definition for L.
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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I need help in this question of Linear Transformation
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2. Let L: R4 R3 be defined by
L ([u₁ U₂ Uz
u4]) = [u₁ u₂+ Uz
Uz + U₁]
Let S and T be the natural bases for R4 and R3, respectively. Let
{[10 0 1], [0 0 0 1],[1 1 0 0], [0 1 1 0]}
and I' {[1 1 0], [0 1 0],[1
0 1]}
S' =
(a) Find the representation of L with respect to S and T.
(b) Find the representation of L with respect to S' and T'.
(c) Find L([2 1 -1 3]) by using the matrices obtained in parts
(a) and (b) and compare this answer with that obtained from the
definition for L.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0cfa59ce-5074-4e94-af68-42c59c01b835%2Fd64dcf4f-566d-408e-8d44-bc73b6cb42ee%2Fj5zcvr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:T
2. Let L: R4 R3 be defined by
L ([u₁ U₂ Uz
u4]) = [u₁ u₂+ Uz
Uz + U₁]
Let S and T be the natural bases for R4 and R3, respectively. Let
{[10 0 1], [0 0 0 1],[1 1 0 0], [0 1 1 0]}
and I' {[1 1 0], [0 1 0],[1
0 1]}
S' =
(a) Find the representation of L with respect to S and T.
(b) Find the representation of L with respect to S' and T'.
(c) Find L([2 1 -1 3]) by using the matrices obtained in parts
(a) and (b) and compare this answer with that obtained from the
definition for L.
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