Let V = R³, U = {(x, y, z) = R³ | 3x + y − 5z = 0} and W = {(x, y, 0) ≤ R³ | x + 2y = 0}.Which of the following applies to Un Wand U + W?Select one:None of the others applyOun W is a line, U + W = VO UnW = {0},U+W = VUnW=W, U + W = UUnW is a line, U+W is a plane

Let , , and .Which of the following applies to and ?a. None of the others apply.b. is a line, .c.…

Answered: Let V = R³, U = {(x, y, z) = R³ | 3x +…

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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Question

Let V = R³, U = {(x, y, z) = R³ | 3x + y − 5z = 0} and W = {(x, y, 0) ≤ R³ | x + 2y = 0}.
Which of the following applies to Un Wand U + W?
Select one:
None of the others apply
O
un W is a line, U + W = V
O UnW = {0},U+W = V
UnW=W, U + W = U
UnW is a line, U+W is a plane

Expert Solution

Step 1: Question Description

Let $V equals straight real numbers cubed$ , $U equals open curly brackets open parentheses x comma y comma z close parentheses element of straight real numbers cubed space vertical line space 3 x plus y minus 5 z equals 0 close curly brackets$ , and $W equals open curly brackets open parentheses x comma y comma 0 close parentheses element of straight real numbers cubed space vertical line space x plus 2 y equals 0 close curly brackets$ .

Which of the following applies to $U intersection W$ and $U plus W$ ?

a. None of the others apply.

b. $U intersection W$ is a line, $U plus W equals V$ .

c. $U intersection W equals open curly brackets 0 close curly brackets$ , $U plus W equals V$

d. $U intersection W equals W$ , $U plus W equals V$ .

e. $U intersection W$ is a line, $U plus W$ is a plane.