Let {v1,v2,···,vn}be a set of linearly dependent vectors in Rn. Show that there exists an n×n matrix A such that for any x∈Rn, j= 1,2,···n, we have [Ax]j=x·vj. Also, find a vector u∈Rn\C(A). 9.Let {v1, v2,, Vn} be a set of linearly dependent vectors in R". Show that there exists ann x n matrix A such that for any x E R", j = 1, 2, · . · n, we have [Ax]; = x · vj. Also, find a vectoru E R" \ C(A).

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Let {v1,v2,···,vn}be a set of linearly dependent vectors in Rn. Show that there exists an n×n matrix A such that for any x∈Rn, j= 1,2,···n, we have [Ax]j=x·vj. Also, find a vector u∈Rn\C(A)

Let {v1,v2,···,vn}be a set of linearly dependent vectors in Rn. Show that there exists an n×n matrix A such that for any x∈Rn, j= 1,2,···n, we have [Ax]j=x·vj. Also, find a vector u∈Rn\C(A)

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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