Finding Pivots in Row Reduction: Does a Zero on Top Matter?

Thread starter magma_saber
Start date Apr 1, 2009
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Matrix Reduction Row

In summary, matrix row reduction, also known as Gaussian elimination, is a method used to simplify a matrix and solve systems of linear equations, find inverse matrices, and determine the rank of a matrix. To perform matrix row reduction, follow these steps: start with the original matrix, choose a pivot element, use row operations to make all other elements in the same column as the pivot element equal to 0, move to the next row and repeat the process until the matrix is in row-echelon form, and if necessary, use back substitution to find the values of the variables. Matrix row reduction can be used for matrices of any size, but may be more complex for larger matrices. However, it may not be applicable for matrices with a

Apr 1, 2009

magma_saber

Homework Statement

When row reducing and trying to find the pivots, does it matter if there is a zero on top?
i.e.:
1 2 3 4
0 8 0 5
0 0 4 6

i know that the 1st and 2nd columns are pivots but is the 3rd column a pivot also?

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Apr 1, 2009

ascapoccia

no, it doesn't matter. It is still a pivot.

1. What is matrix row reduction and why is it important?

Matrix row reduction, also known as Gaussian elimination, is a method used to simplify a matrix by transforming it into a row-echelon form. This process is important because it allows us to solve systems of linear equations, find inverse matrices, and determine the rank of a matrix.

2. How do I perform matrix row reduction?

To perform matrix row reduction, follow these steps:

Start with the original matrix.
Choose a pivot element, usually the first non-zero element in the first row.
Use row operations to make all other elements in the same column as the pivot element equal to 0.
Move to the next row and repeat the process until the matrix is in row-echelon form.
If necessary, use back substitution to find the values of the variables.

3. Can I use matrix row reduction for matrices of any size?

Yes, matrix row reduction can be used for matrices of any size. However, the process may be more complex for larger matrices.

4. Are there any limitations to matrix row reduction?

Matrix row reduction may not be applicable for matrices that have a determinant of 0, as these matrices are not invertible and cannot be reduced to row-echelon form.