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 linearlyindependent set of vectors in R3c) Determine whether W = {(x, y, z) E R³| x² + y² = z?} is a subspace ofR3

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Answered: a) Determine whether S = {(1,0,-1),…

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 30EQ

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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

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