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Pivot columns in a Matrix

  • Thread starter flyingpig
  • Start date
  • #1
2,571
1

Homework Statement




Just need help identifying pivots columns

[tex]\begin{bmatrix}
1 & 1 & 1 &1 &1\\
0& 0& 0& 0&0\\
0& 0& 0& 0&9
\end{bmatrix}[/tex]

From my understanding, any column with 1s and everything below it 0s are all pivot columns right?

Is the above all pivot columns? Also for a 3 x 5 coefficent matrix that has three pivot columns, is the system consistent?

The book says it is not, but why? The one above is a counterargument given by me. Does anyone know the LaTeX code to make an augmented matrix? Like put a bar before the constants
 

Answers and Replies

  • #2
2,571
1
The last column number should be a 0 not 9
 
  • #3
remember, the definition of a pivot column is essentially that the column contains a pivot position in reduced echelon form. a pivot is the first nonzero term in the row (which needs to be a 1 for it to be reduced echelon form). how many of your rows in that matrix have a pivot in them?
 
Last edited:
  • #4
2,571
1
There can only be one pivot column in every row?
 
  • #5
There can only be one pivot position in each row. Notice that there is a subtle difference between a pivot column and a pivot itself.
 

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