Finding a Basis for Subspace in R^4: Linear Algebra Tips

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Homework Help Overview

The discussion revolves around finding a basis for a subspace in R^4, specifically focusing on a set of four vectors. Participants are exploring methods to determine linear independence and span of the given vectors.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss setting up the vectors as columns in a matrix and performing row reduction to check for linear independence. There are inquiries about the process of row reducing and the implications of the reduced row echelon form (RREF). Some participants mention the determinant as a criterion for linear dependence.

Discussion Status

The discussion is active, with various approaches being considered. Some participants have attempted row reduction and shared their findings, while others are still questioning the setup and implications of their methods. There is no explicit consensus yet on the outcome of the basis determination.

Contextual Notes

Participants are working within the constraints of linear algebra principles, specifically regarding vector spaces and linear combinations. The original poster's intent to test for independence is noted, as well as the importance of determining pivots in the matrix.

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Help! Find a basis.
Find a basis for the subspace of R^4 spanned by, S={(6,-3,6,340, (3,-2,3,19), (8,3,-9,6), (-2,0,6,-5)

Figured I would set up the linear combination to test for independence.
 
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Do you know how to set up these four vectors as columns to make a 4x4 matrix?

Have you done row reducing?

Because that would also be an approach to determining if they are linearly independent.
 
I made up the columns, solved for rref, and came up with the trivial solution
 
As long as you got it to RREF, then you can see if there is a pivot in each column, if there is, then these vectors span R4. If there is not a pivot in each, then they do not span R4.

Good luck!
 
If the determinant of the matrix these vectors make is 0 then some of them are linearly dependent.
 

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