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Let be the set A = {(2, –2,6), (1,2,0), (3,0,6)}, of vectors of R³ a) Determine the vector space w (generic element) that is spanned by the set A. b) Obtain the standard base and the dimension of w. c) State whether the vector (-1,1, –3) belongs to the space w.

Let be the set A = {(2, –2,6), (1,2,0), (3,0,6)}, of vectors of R³ a) Determine the vector space w (generic element) that is spanned by the set A. b) Obtain the standard base and the dimension of w. c) State whether the vector (-1,1, –3) belongs to the space w.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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Let be the set A = {(2, –2,6), (1,2,0), (3,0,6)}, of vectors of R a) Determine the vector space w (generic element) that is spanned by the set A. b) Obtain the standard base and the dimension of w. c) State whether the vector (-1,1, –3) belongs to the space W.
Transcribed Image Text:Let be the set A = {(2, –2,6), (1,2,0), (3,0,6)}, of vectors of R a) Determine the vector space w (generic element) that is spanned by the set A. b) Obtain the standard base and the dimension of w. c) State whether the vector (-1,1, –3) belongs to the space W.
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