The row echelon form of a matrix is a particular form obtained through a sequence of elementary row operations. It is characterized by the following properties:

  1. The first non-zero entry in each row, called the leading entry or pivot, is always strictly to the right of the leading entry in the row above.

  2. Any rows consisting entirely of zeros are at the bottom of the matrix.

  3. Each pivot is equal to 1.

  4. All entries below and above each pivot are zeros.

  To transform a matrix into row echelon form, you can perform the following elementary row operations:

  1. Interchanging two rows.

  2. Multiplying a row by a non-zero scalar.

  3. Adding a scalar multiple of one row to another row.

  The row echelon form is useful for solving systems of linear equations, finding the rank of a matrix, and computing the inverse of a matrix.

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