What Determines Pivot Positions in a Matrix?

In summary, the given matrix has been reduced to echelon form, with the pivot positions marked as X. The first three columns are pivot columns. The bonus question asks for a basis of the column space and row space of the given matrix, which is a set of linearly independent vectors that can represent every vector in the respective space. To check for linear independence, we can use the determinant method or the rank method.
  • #1
NorwegianStud
5
0
Matrix: Ã=
1 -2 0 0 3
2 -5 -3 -2 6
0 5 15 10 0
2 6 18 8 6

Matrix on reduced echelon form:
1 0 0 -2 3
0 1 0 -1 0
0 0 1 1 0
0 0 0 0 0

X 0 0 -2 3
0 X 0 -1 0
0 0 X 1 0
0 0 0 0 0

Are the pivot positions the ones I've marked with X? And therefor colum 1, 2 and 3 are pivot columns? Or have I completely misunderstood?
Bonus question: Can't work out "Find a basis for Col(Ã), Row(Ã)". What does that even mean?
 
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  • #2
Those are indeed the pivots.

As for the bonus, the basis is just a set of linearly independent vectors that can represent every vector in a space.
 
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  • #3
QuarkCharmer said:
Those are indeed the pivots.

As for the bonus, the basis is just a set of linearly independent vectors that can represent every vector in a space.

Great, thanks a lot.

Linearly independent vectors? I've seen that before when I looked for the answer, but I didn't quite understand it. How do I check if it's linearly independent?
 

FAQ: What Determines Pivot Positions in a Matrix?

What is a quick Pivot column question?

A quick Pivot column question refers to a type of data analysis technique in which a table of data is transformed to display data from rows as columns or vice versa. This allows for easier manipulation and analysis of large datasets.

How is a quick Pivot column question different from a regular Pivot question?

The main difference between a quick Pivot column question and a regular Pivot question is the speed at which the data can be transformed. A quick Pivot column question is designed to be faster and more efficient for simple data transformations, while a regular Pivot question allows for more complex and customizable transformations.

What types of data can be used in a quick Pivot column question?

A quick Pivot column question can be used with any type of tabular data, including numerical, categorical, and textual data. It is also compatible with data from various sources, such as spreadsheets, databases, and online data repositories.

How do I create a quick Pivot column question?

To create a quick Pivot column question, you can use a spreadsheet program or specialized data analysis software. Simply select the data you want to transform, and choose the quick Pivot column option. You can then customize the layout and calculations to suit your needs.

What are the benefits of using a quick Pivot column question?

The main benefit of using a quick Pivot column question is the ability to quickly and easily transform data for analysis. This can save time and effort, especially when dealing with large datasets. Additionally, a quick Pivot column question can help identify patterns and relationships in the data that may not be apparent in its original form.

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