Determining Pivot Columns in a Matrix - Fred's Question

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Homework Help Overview

The discussion revolves around identifying pivot columns in a matrix, specifically in the context of row echelon form and Gaussian elimination. The original poster, Fred, seeks clarification on how to determine if a column qualifies as a pivot column.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of pivot columns and question the criteria for identifying them in the context of a given matrix. There is a discussion about the relationship between non-zero entries and their positions in the matrix.

Discussion Status

The discussion is active, with participants providing differing interpretations of what constitutes a pivot column. Some guidance has been offered regarding the identification of pivot columns in row echelon form, but there is no explicit consensus on the correct columns based on the examples provided.

Contextual Notes

Participants are working with a specific matrix example and its echelon form, which may influence their interpretations of pivot columns. There is an underlying assumption about the definitions and rules of matrix operations that is being examined.

mathboy20
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Hi

I got simple question. How is it that determain if a column in matrix is a pivot column?

Sincerely

Fred
 
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mathboy20 said:
I got simple question. How is it that determain if a column in matrix is a pivot column?

Are you asking about gaussian reduction, the simplex method, or something else?
 
NateTG said:
Are you asking about gaussian reduction, the simplex method, or something else?

What I'm asking given a matrix

A= [[1,2,2,0,1,1][0,i,0,0,1,2][0,0,0,0,i,0][0,0,1,2,2i]]


Which in echelonform gives

A ~[[1,2,2,0,1,1][0,1,0,0,-i,-2i][0,0,1,2,0,2i][0,0,0,0,1,0]]

My question is the pivot column of this matrix aren't they

column 1,2,5,6 ??

Since the definition a pivot position is is the column where there is a non-zero entry above a zero entry??

Best Regards
Mathboy20
 
For row echelon form, the pivot columns where there is a non-zero value to the right of leading zeros.

In the example you give, the pivot columns would be 1,2,3, and 5.
 

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