||Homework Help||Kindergarten-University. - Page 11

The rank of a matrix is the maximum number of independent rows (or, the maximum number of independent columns).

1 2 0 3
1 7 3 0
0 0 4 8
2 4 0 6

Start with row 1: See if row 2, 3 or 4 are multiples. If so, cross that out.
Go to row 2: See if row 3 or 4 are multiples...
Finally compare row 3 and 4.

This is for 4 rows, but you can extend this to n rows.

Do the same for the columns.

The rank would be 3 in the example above because we crossed out a row, leaving 3. The last row is a multiple of the first.