Final answer:
The statement that two matrices are row equivalent if they have the same number of rows is false. Row equivalence is about the ability to transform matrices into each other through row operations, not merely about the number of rows.
Step-by-step explanation:
Two matrices are row equivalent if they can be transformed into one another by a sequence of row operations, which include row switching, row multiplication, and row addition. The statement in question, 'Two matrices are row equivalent if they have the same number of rows', is False. Matrices can have the same number of rows but not be row equivalent if they cannot be transformed into one another through row operations. Similarly, having a different number of rows automatically means that they aren't row equivalent, as the operations cannot be consistently applied.