1. Consider the following subspaces of R³: U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R} (a) (b) W). Find UnW. Is U + W a direct sum (and why)? And, find dim(U+
1. Consider the following subspaces of R³: U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R} (a) (b) W). Find UnW. Is U + W a direct sum (and why)? And, find dim(U+
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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![1. Consider the following subspaces of R³:
(a)
(b)
U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R}
W).
Find UnW.
Is U + W a direct sum (and why)? And, find dim(U +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2F017cca3e-4b34-42b7-9626-99e370c9e060%2Fuil4m6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the following subspaces of R³:
(a)
(b)
U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R}
W).
Find UnW.
Is U + W a direct sum (and why)? And, find dim(U +
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Don't change the W subspace. It is W = {(x,-x, 2x): x, y ≤ R}
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