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0,−1), (2,1,0), (3,1,-1), (1,1,1)} spans. {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly R³. y, z) € R³| x² + y² = z²} is a subspace

0,−1), (2,1,0), (3,1,-1), (1,1,1)} spans. {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly R³. y, z) € R³| x² + y² = z²} is a subspace

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 38EQ
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a) Determine whether S = {(1,0, – 1), (2,1,0), (3,1, – 1), (1,1,1)} spans. R³. {(c2,0,1), (0, c, 0), (1,2,1)} is a linearly b) Find all c ER for which s independent set of vectors in R³. c) Determine whether W = {(x, y, z) E R°| x² + y? = z?} is a subspace of R³. =
Transcribed Image Text:a) Determine whether S = {(1,0, – 1), (2,1,0), (3,1, – 1), (1,1,1)} spans. R³. {(c2,0,1), (0, c, 0), (1,2,1)} is a linearly b) Find all c ER for which s independent set of vectors in R³. c) Determine whether W = {(x, y, z) E R°| x² + y? = z?} is a subspace of R³. =
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