Identifying Redundant Vectors from a 1x4 Matrix

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    Matrix Vectors
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Homework Help Overview

The discussion revolves around identifying redundant vectors from a set of four vectors represented as a 1x4 matrix. The subject area pertains to linear algebra, specifically concepts of linear independence and spanning sets in vector spaces.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of linear independence to determine if any vectors can be removed without altering the span. Questions arise regarding the criteria for a set of vectors to form a basis for R^4 and the implications of independence on spanning.

Discussion Status

The discussion is active, with participants providing guidance on checking linear independence as a method to assess redundancy. Multiple interpretations of the properties of a basis are being explored, particularly regarding the relationship between independence and spanning.

Contextual Notes

Participants are considering the implications of having four vectors in relation to the dimensionality of R^4, as well as the necessary conditions for a set of vectors to be a basis.

Derill03
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im given four vectors as a 1x4 matrices:

[1,4,2,8]^t = v1
[2,5,3,9]^t = v2
[11,14,12,18]^t = v3
[4,3,2,1]^t = v4

How can i know which if any of these vectors can be removed without changing the span?
 
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Check if they're linearly independent. If they are, then you cannot remove any of them without changing the span.
 
How can i tell if the vectors are a basis for R^4?
 
A basis for an n dimensional vector space has three properties
1) the vectors span the space
2) the vectors are independent
3) the set contains n vectors

and, any two of those is sufficient to prove the third.

You know you have four vectors here. If they are independent, then they must also span the space and are a basis. If they are not independent, they do not form a basis.
 

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