x1 x2 Let W be the subset of R4 consisting of all vectors such that 1-2x2 = 4x3 and 2x1 = x3 + 3x4. x3 x4 Determine if W is a subspace of R4 and check the correct answer(s) below. A. W is a subspace because it can be written as N(A) for some matrix A. B. W is not a subspace because it does not have a zero element. C. W is not subspace because it does not have additive closure. D. W is a subpace because it has a zero element.

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
x1
x2
Let W be the subset of R4 consisting of all vectors
such that 1
=
-
2x24x3 and 2x1
= x3 + 3x4.
x3
24
Determine if W is a subspace of R¹ and check the correct answer(s) below.
A. W is a subspace because it can be written as N(A) for some matrix A.
B. W is not a subspace because it does not have a zero element.
C. W is not subspace because it does not have additive closure.
D. W is a subpace because it has a zero element.
Transcribed Image Text:x1 x2 Let W be the subset of R4 consisting of all vectors such that 1 = - 2x24x3 and 2x1 = x3 + 3x4. x3 24 Determine if W is a subspace of R¹ and check the correct answer(s) below. A. W is a subspace because it can be written as N(A) for some matrix A. B. W is not a subspace because it does not have a zero element. C. W is not subspace because it does not have additive closure. D. W is a subpace because it has a zero element.
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