Understanding Row Echelon Form and Reduced Row Echelon Form in Matrices | Explained and Compared

If a matrix is in reduced row echelon form, then it is also in row echelon form.

A matrix is said to be in row echelon form if it follows these conditions:

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A matrix is said to be in row echelon form if it follows these conditions:

1. The first non-zero entry in each row, also known as the leading entry, is to the right of the leading entry in the row above it.
2. Any rows consisting entirely of zeros are at the bottom (if any).
3. All entries in a column below and above the leading entry are zeros.

Reduced row echelon form, on the other hand, is a stricter form of row echelon form that follows additional conditions:

1. The leading entry in each row is always 1.
2. The leading 1 in each row is the only non-zero entry in its column.
3. All rows above and below the leading 1 are zeros.

In summary, every matrix that is in reduced row echelon form is also in row echelon form. This is because the conditions for row echelon form are satisfied and reduced row echelon form adds extra conditions to ensure further simplification and uniqueness of the matrix.

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