a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,−1), (1,1,1)} spans R³. b) Find all c ER for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly independent set of vectors in R³ c) Determine whether W = {(x, y, z) € R³ | x² + y² = z²} is a subspace of R³
a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,−1), (1,1,1)} spans R³. b) Find all c ER for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly independent set of vectors in R³ c) Determine whether W = {(x, y, z) € R³ | x² + y² = z²} is a subspace of R³
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 35EQ
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a) Determine whether S={(1,0,-1),(2,1,0),(3,1,-1),(1,1,1)} spans R^3.
b) Determine whether W={(x,y,z)∈R^3│ x^2+y^2=z^2 } is a subspace of R^3.
c) Find all c∈R for which S={(c^2,0,1),(0,c,0),(1,2,1)} is a linearly independent set of vectors in R^3.
![a) Determine whether S = {(1,0,–1), (2,1,0), (3,1, –1), (1,1,1)} spans R³.
|3|
b) Find all c ER for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly
independent set of vectors in R3
c) Determine whether W = {(x, y, z) E R³| x² + y² = z?} is a subspace of
R3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3fe88fe-1de6-4b0f-9f96-618a709bdbcf%2Fdb4eff16-7833-44bb-a18f-1957a81bdd03%2Fjha0y7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Determine whether S = {(1,0,–1), (2,1,0), (3,1, –1), (1,1,1)} spans R³.
|3|
b) Find all c ER for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly
independent set of vectors in R3
c) Determine whether W = {(x, y, z) E R³| x² + y² = z?} is a subspace of
R3
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