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Echelon Form and Reduced Echelon Form of a Matrix | Naimat Maths

What is Echelon Form?
Echelon form means that the matrix is in one of two states:

Row echelon form.
Reduced row echelon form.
This means that the matrix meets the following three requirements:

The first number in the row (called a leading coefficient) is 1. Note: some authors don’t require that the leading coefficient is a 1; it could be any number. You may want to check with your instructor to see which version of this rule they are adhering to).
Every leading 1 is to the right of the one above it.
Any non-zero rows are always above rows with all zeros.

Uniqueness and Echelon Forms:

The echelon form of a matrix isn’t unique, which means there are infinite answers possible when you perform row reduction. Reduced row echelon form is at the other end of the spectrum; it is unique, which means row-reduction on a matrix will produce the same answer no matter how you perform the same row operations.
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What is Row Echelon Form?
A matrix is in row echelon form if it meets the following requirements:
The first non-zero number from the left (the “leading coefficient“) is always to the right of the first non-zero number in the row above.
Rows consisting of all zeros are at the bottom of the matrix.

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