Question

Which of the following statements are true and which are false? Justify your answer with a
short proof or a counterexample.

The rank of a matrix equals its number of nonzero rows.

Answer 1

The statement is false. For example, in matrix rows 1 1 and 2 2 are nonzero, but the rank of matrix is 1, which is not equal to 2 (its number of nonzero rows).