Let S={<5,2,-5>,<7,-3,2>,<13,1,-8>,<9,6,-15>} a Decide whether or not the vector b=<2,0,0> is a member of Span(S). !f b is indeed a member of Span(S), then express it as a linear combination of the vectors in S. с. Is the set S linearly independent or not? Explain your answer. d. Give a basis for W=Span(S) consisting of original members of S.
Let S={<5,2,-5>,<7,-3,2>,<13,1,-8>,<9,6,-15>} a Decide whether or not the vector b=<2,0,0> is a member of Span(S). !f b is indeed a member of Span(S), then express it as a linear combination of the vectors in S. с. Is the set S linearly independent or not? Explain your answer. d. Give a basis for W=Span(S) consisting of original members of S.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1.
Give complete definitions of the following terms.
a.a linear combination of v,...,V_{k}
b.the Span of a set of vectors S={v,...,v_{k}}
c.a linearly independent set S={v,.v_{k}}
d.a subspace W
e.the orthogonal complement of a subspace W of R".
f.a basis for W
2
Indicate if the statement is True or False, and give a brief explanation
why.
a.A set of 7 vectors from a 7-dimensional subspace is linearly independent.
b.A set of 11 vectors from an 5-dimensional subspace is linearly dependent.
c.lf S={v,,V2} is a set of two non-zero vectors from R', then Span(S) is a line or a plane through
the origin.
Let S={<5,2,-5>,<7,-3,2>,<13,1,-8>,<9,6,-15>}
a
Decide whether or not the vector b=<2,0,0> is a member of Span(S).
'f b is indeed a member of Span(S), then express it as a linear combination of the
vectors in S.
с.
Is the set S linearly independent or not? Explain your answer.
d.
Give a basis for W=Span(S) consisting of original members of S.
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