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a. The union of two subspaces of a vector space is always a subspace. b. The basis for the zero vector space {0} consists of the zero vector itself. c. There exist vectors u,v,w E R^3 (R = real numbers) such that u-v,v-w,w-u span R^3 (R = real numbers) d. If S is a linearly independent set and T is a spanning set in a vector space V, then SOT is a basis for V. e. A subset of a spanning set can sometimes form a linearly independent set

a. The union of two subspaces of a vector space is always a subspace. b. The basis for the zero vector space {0} consists of the zero vector itself. c. There exist vectors u,v,w E R^3 (R = real numbers) such that u-v,v-w,w-u span R^3 (R = real numbers) d. If S is a linearly independent set and T is a spanning set in a vector space V, then SOT is a basis for V. e. A subset of a spanning set can sometimes form a linearly independent set

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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Are the following statements true or false?

a. The union of two subspaces of a vector space is always a subspace. b. The basis for the zero vector space {0} consists of the zero vector itself. c. There exist vectors u,v,w E R^3 (R = real numbers) such that u-v,v-w,w-u span R^3 (R = real numbers) d. If S is a linearly independent set and T is a spanning set in a vector space V, then SOT is a basis for V. e. A subset of a spanning set can sometimes form a linearly independent set
Transcribed Image Text:a. The union of two subspaces of a vector space is always a subspace. b. The basis for the zero vector space {0} consists of the zero vector itself. c. There exist vectors u,v,w E R^3 (R = real numbers) such that u-v,v-w,w-u span R^3 (R = real numbers) d. If S is a linearly independent set and T is a spanning set in a vector space V, then SOT is a basis for V. e. A subset of a spanning set can sometimes form a linearly independent set
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