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Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i ≤n) is equal to 0 (nil), while all other elements are equal to 1. Do these n vectors form a basis of this n- space? Suppose we have k

Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i ≤n) is equal to 0 (nil), while all other elements are equal to 1. Do these n vectors form a basis of this n- space? Suppose we have k

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
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Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i ≤n) is equal to 0 (nil), while all other elements are equal to 1. Do these n vectors form a basis of this n-space? Suppose we have k <n linearly independent vectors in R" vector space. Do these k vectors completely span the n-space? If not, what's the highest dimension in Euclidean space that these k < n vectors span? True or false: the following 2 vectors form a basis of the R³ vector space? (-)-() True or false: the following 3 vectors form a (not the) basis of the R³ vector space? 0.0.0
Transcribed Image Text:Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i ≤n) is equal to 0 (nil), while all other elements are equal to 1. Do these n vectors form a basis of this n-space? Suppose we have k <n linearly independent vectors in R" vector space. Do these k vectors completely span the n-space? If not, what's the highest dimension in Euclidean space that these k < n vectors span? True or false: the following 2 vectors form a basis of the R³ vector space? (-)-() True or false: the following 3 vectors form a (not the) basis of the R³ vector space? 0.0.0
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