(B3) let V1, V2, . , Vn vectors in R". For all 1si, jsn, suppose that 1, si i= j, %3D 0, si i+ j, k=1 where (vi)k is the k-th component of Vi- %3D Vi (a) Show that (b) Show that the vectors v1, v2, ..., vn are linearly independent. where and Vj'are column vectors.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...
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V1, V2, . , Vn
vectors in R".
For all 1 si, js n, suppose that
(B3) let
1, si i= j,
%3D
0, si i+ j,
k=1
(vi)k
is the k-th component of V.
where
(a) Show that
(b) Show that the vectors v1, v2, ..., vn are linearly independent.
Vi
where
and 'are column vectors.
Transcribed Image Text:V1, V2, . , Vn vectors in R". For all 1 si, js n, suppose that (B3) let 1, si i= j, %3D 0, si i+ j, k=1 (vi)k is the k-th component of V. where (a) Show that (b) Show that the vectors v1, v2, ..., vn are linearly independent. Vi where and 'are column vectors.
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