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Yes, elementary row operations preserve the rank. Reducing a matrix toward echelon form reveals which rows contain pivots and which become zero, allowing the rank to be counted without changing the underlying linear dependencies.

Conditions: The operations are elementary row operations (swapping rows, scaling rows, adding multiples of one row to another).

Yes, elementary row operations preserve the rank. Reducing a matrix toward echelon form reveals which rows contain pivots and which become zero, allowing the rank to be counted without changing the underlying linear dependencies.

Conditions: The operations are elementary row operations (swapping rows, scaling rows, adding multiples of one row to another).