# Linear algebra - rank

## Homework Statement

Find the rank of A =
{[1 0 2 0]
[4 0 3 0]
[5 0 -1 0]
[2 -3 1 1]}

## The Attempt at a Solution

i row reduced A to be:
{[1 0 0 0]
[0 1 0 -1/3]
[0 0 1 0]}

where do i go from here?

Dick
Homework Helper
I think you omitted a last row of zeros. Ok, what does rank mean?

The column rank of a matrix A is the maximal number of linearly independent columns of A. Likewise, the row rank is the maximal number of linearly independent rows of A.

Since the column rank and the row rank are always equal, they are simply called the rank of A.

Dick
Homework Helper
The column rank of a matrix A is the maximal number of linearly independent columns of A. Likewise, the row rank is the maximal number of linearly independent rows of A.

Since the column rank and the row rank are always equal, they are simply called the rank of A.

Good! So how many linearly independent rows are there? If you have no idea, quote the definition of linear independence.

so is it 3? because the 2nd and 4th columns are dependent.

Dick