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Let V=R° be the vector space of ordered 6-tuples of real numbers with the usual addition and scal %3D Let W be the subspace of all vectors of form (a, b, a, c, a-3b, b+ c) in V. Which of following statements are True? Select ALL that apply. O dim(W) = 3 %3D O {e1, e2, e3} is a basis for W D {(1,0, 1,0, 1,0), (0, 1,0,0, -3, 1), (0,0,0, 1,0,1)} is a basis for W O dim(W) = 6

Let V=R° be the vector space of ordered 6-tuples of real numbers with the usual addition and scal %3D Let W be the subspace of all vectors of form (a, b, a, c, a-3b, b+ c) in V. Which of following statements are True? Select ALL that apply. O dim(W) = 3 %3D O {e1, e2, e3} is a basis for W D {(1,0, 1,0, 1,0), (0, 1,0,0, -3, 1), (0,0,0, 1,0,1)} is a basis for W O dim(W) = 6

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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math editoe. Quention 25 Let V=R° be the vector space of ordered 6-tuples of real numbers with the usual addition and scalar multiplication. Let W be the subspace of all vectors of form (a, b, a, c, a-3b, b+ c) in V. Which of following statements are True? Select ALL that apply. O dim(W) = 3 O {e1; e2, e3} is a basis for W O {(1,0, 1,0, 1,0), (0, 1,0,0, –3, 1), (0,0,0, 1,0, 1)} is a basis for W O dim(W) = 6 • Previous
Transcribed Image Text:math editoe. Quention 25 Let V=R° be the vector space of ordered 6-tuples of real numbers with the usual addition and scalar multiplication. Let W be the subspace of all vectors of form (a, b, a, c, a-3b, b+ c) in V. Which of following statements are True? Select ALL that apply. O dim(W) = 3 O {e1; e2, e3} is a basis for W O {(1,0, 1,0, 1,0), (0, 1,0,0, –3, 1), (0,0,0, 1,0, 1)} is a basis for W O dim(W) = 6 • Previous
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