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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
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 +
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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