In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. Is this statement true or false?

Question

Mathematics

Kaeden

12 November, 00:56

In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. Is this statement true or false?

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Answers (1)

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Armando Mcgrath · Answer 1

This is False.

Step-by-step explanation:

To solve matrices, operations such as the Gaussian elimination can be used. After this operation, a matrix with a row echelon form is obtained. The reduced echelon form is particular case of this, in which the matrix:

1. Is in row echelon form.

2. The first number in each non-zero row is 1 (which is called a leading 1).

3. Each column that has a leading 1 has zeros everywhere else

A matrix in a reduced row echelon form is unique and independent on the algorithm used to calculate it.