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1. Determine if the set {(1, -2, 3), (7, 4, -2), (3, -6, 9)} is linearly dependent.

1. Determine if the set {(1, -2, 3), (7, 4, -2), (3, -6, 9)} is linearly dependent.

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. Determine if the set {(1, -2, 3), (7, 4, -2), (3, -6, 9)} is linearly dependent. 2. Determine if the set {(1, 1, 1), (2, 2, -2), (0, 1, 5)} linearly independent. 3. Find values of h for which the set {(3, h), (6, h-1)} is linearly dependent. 4. Let g(x) = 2x² + 3 and h(x) = x² + 3x - 1. Is the function f(x) = 3x² + 5x + 1 in the subspace Span{g, h} of P₂? 5. Is the set {(a, b, c) la = b + c} a subspace of R³?
Transcribed Image Text:1. Determine if the set {(1, -2, 3), (7, 4, -2), (3, -6, 9)} is linearly dependent. 2. Determine if the set {(1, 1, 1), (2, 2, -2), (0, 1, 5)} linearly independent. 3. Find values of h for which the set {(3, h), (6, h-1)} is linearly dependent. 4. Let g(x) = 2x² + 3 and h(x) = x² + 3x - 1. Is the function f(x) = 3x² + 5x + 1 in the subspace Span{g, h} of P₂? 5. Is the set {(a, b, c) la = b + c} a subspace of R³?
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