Q-2: a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,-1), (1,1,1)} spans R. 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 R. c) Determine whether W = {(x, y, z) E R°| x² + y² = z²} is a subspace of R³.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Q-2:
a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,-1), (1,1,1)} spans R.
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 R².
c) Determine whether W = {(x, y, z) E R°| x² +y2 = z?} is a subspace of
R.
Transcribed Image Text:Q-2: a) Determine whether S = {(1,0,-1), (2,1,0), (3,1,-1), (1,1,1)} spans R. 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 R². c) Determine whether W = {(x, y, z) E R°| x² +y2 = z?} is a subspace of R.
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