Matrix Echelon And Reduced Echelon Form For Efficient Algebraic Operations

When is a matrix in echelon form? Reduced form?

1.) Any and all zero rows are at the bottom.2.) The first non-zero (leading) entry of a row is to the right of any leading entries in the row above it. 3.) Below a leading entry, all entries are zero. ————————————————–4.) The leading entry in each row is 1.5.) Each leading 1 is the only nonzero entry in that column.

A matrix is said to be in echelon form if it has the following properties:

1. All rows consisting entirely of zeros are at the bottom of the matrix.
2. For each row that is non-zero, the first non-zero element is called a pivot or leading coefficient, and it is the only non-zero element in its column.
3. Each pivot is strictly to the right of the pivot of the row above it.

A matrix is said to be in reduced echelon form or row-reduced echelon form if it has the following properties:

1. It is already in echelon form.
2. Each pivot is equal to 1.
3. The columns containing pivots have zeros everywhere else.

So, a matrix is said to be in echelon form if it satisfies criteria 1-3 above, and it is said to be in reduced echelon form if it satisfies all five criteria.

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