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Row Echelon and Column Echelon Matrix

1. Any \(M \times N\) (where \(M \geq 2\) and \(N \geq 2\)) Matrix is said to be in Row Echelon Form if All the following 3 conditions are True
   1. All the Zero Values Must Preceed Any Non-Zero Value for all the Rows/Co-Vectors.
   2. All the Non-Zero Values Must Preceed Any Zero Value for all the Columns/Vectors.
   3. First Column/Vector Must have One and Only One Non Zero Value. Any Succeeding Columns/Vectors have Atleast as many Non-Zero Values as the Previous Column/Vector and Atmost One Non-Zero Value More than the Previous Column/Vector.
   Hence, the Row Echelon Matrices have all the Zero Values Concentrated at the Bottom and Left Corner of the Matrix while the Non-Zero Values are Concentrated at the Top and Right Corner of the Matrix.
2. Any \(M \times N\) (where \(M \geq 2\) and \(N \geq 2\)) Matrix is said to be in Column Echelon Form if All the following 3 conditions are True
   1. All the Zero Values Must Preceed Any Non-Zero Value for all the Columns/Vectors.
   2. All the Non-Zero Values Must Preceed Any Zero Value for all the Rows/Co-Vectors.
   3. First Row/Co-Vector Must have One and Only One Non Zero Value. Any Succeeding Rows have Atleast as many Non-Zero Values as the Previous Row/Co-Vector and Atmost One Non-Zero Value More than the Previous Row/Co-Vector.
   Hence, the Columns Echelon Matrices have all the Zero Values Concentrated at the Top and Right Corner of the Matrix while the Non-Zero Values are Concentrated at the Bottom and Left Corner of the Matrix.
3. Any \(M \times N\) (where \(M \geq 2\) and \(N \geq 2\)) Matrix can Converted to a Row Echelon or Column Echelon Matrix using the Algorithm for Elementary Row/Column Operations on Matrix.