Row Echelon And Reduced Row Echelon Form In Matrices.

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

1

Yes, this statement is true.

In row echelon form, a matrix satisfies the following conditions:
1. The first non-zero element (also known as the pivot) of each row is to the right of the pivot in the row above it.
2. All elements below the pivot in each column are zero.
3. Rows consisting entirely of zeros are at the bottom.

Reduced row echelon form adds another requirement on top of the row echelon conditions:
4. The pivot of each non-zero row is 1.
5. The pivot is the only non-zero entry in its column.

Any matrix that is in reduced row echelon form also satisfies the conditions of row echelon form. This can be seen by observing that the first non-zero element in each row will be a 1, and all elements below the pivot will be zero. Since each pivot is unique, condition 5 is also satisfied. Therefore, any matrix that is in reduced row echelon form is also in row echelon form.

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