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 subspaceSpan{g, h} of P₂?5. Is the set {(a, b, c) la = b + c} a subspace of R³?

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

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 60E

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Question

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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