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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.