please send complete handwritten solution for Q 1
,<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. "/>
Extracted 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.