Given n vectors V₁,..., Vn, it is possible to write one of the vectors as a lin- ear combination of the other n - 1 vectors if and only if there exist scalars C1,..., Cn, not all zero, such that CIV+CV2+…+C,Vn=0

Given n vectors V₁,..., Vn, it is possible to write one of the vectors as a lin- ear combination of the other n - 1 vectors if and only if there exist scalars C1,..., Cn, not all zero, such that CIV+CV2+…+C,Vn=0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 40E

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Question

Linear algebra: please correctly and in details

Given n vectors V₁,..., Vn, it is possible to write one of the vectors as a lin-
ear combination of the other n - 1 vectors if and only if there exist scalars
C1,..., Cn, not all zero, such that
CIV+CV2+…+CVn=0

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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