2. Let L: R4 –→ R3 be defined by L ([u #2 uz 4]) = [u, uz + u3 uz + u4]. Let S and T be the natural bases for R4 and R3, respec- tively. Let {[! 0 0 1],[00 0 1], [1 1 0 0].[0 1 1 0]} S' and T' = {[1 1 0],[0 1 0],[1 0 1]}. %3D (a) Find the representation of L with respect to S and т.
2. Let L: R4 –→ R3 be defined by L ([u #2 uz 4]) = [u, uz + u3 uz + u4]. Let S and T be the natural bases for R4 and R3, respec- tively. Let {[! 0 0 1],[00 0 1], [1 1 0 0].[0 1 1 0]} S' and T' = {[1 1 0],[0 1 0],[1 0 1]}. %3D (a) Find the representation of L with respect to S and т.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 11AEXP
Related questions
Question
Transcribed Image Text:(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 an-
swer with that obtained from the definition for L.
![2. Let L: R4 R3 be defined by
L ([u u2 uz 44]) = [u1 u2 +uz uz + u4].
Let S and T bc the natural bases for R4 and R3, respec-
tively. Let
S' = {[! 0 0 1].[0 0 0 1].
[1 10 0].[0 1 1 0]}
%3D
and
T' = {[1 1 0],[0 1 0],[1 0 1]}.
(a) Find the representation of L with respect to S and
T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e374a8f-3e11-45e7-b161-3a8dc04326d6%2F380963c4-0c2c-4cbb-b881-4669c135bea3%2Fyfd7tla_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let L: R4 R3 be defined by
L ([u u2 uz 44]) = [u1 u2 +uz uz + u4].
Let S and T bc the natural bases for R4 and R3, respec-
tively. Let
S' = {[! 0 0 1].[0 0 0 1].
[1 10 0].[0 1 1 0]}
%3D
and
T' = {[1 1 0],[0 1 0],[1 0 1]}.
(a) Find the representation of L with respect to S and
T.
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