Linear algebra, rank and nullity

[vs55]

Homework Statement

Find the rank and nullity of the given matrix:

|-2 2 1 1 -2 |----->(1)
|1 -1 -1 -3 3 |----->(2)
|-1 1 -1 7 5 |----->(3)


The attempt at a solution
i know rank is the number of non-zero rows and nullity is the # of columns minus the rank
matrix:
i took (1)+(2) then (1) x -1 to get:
|1 -1 0 2 -1 |
| 1 -1 -1 -3 3 |
|-1 1 -1 7 5 |

(2)+(3)

|1 -1 0 2 -1 |
|0 0 -2 4 8 |
|-1 1 -1 7 5 |

(3)+(1)
|1 -1 0 2 -1 |
|0 0 -2 4 8 |
|0 0 -1 9 4 |

by this the rank should be 3 right? and the nullity is 5-3 = 2

the correct answer is rank 2 and nullity 3
what am i doing wrong?

 

[CompuChip]

You have probably made some calculation errors.

For example, in your first step, instead of
|1 -1 0 2 -1 |
| 1 -1 -1 -3 3 |
|-1 1 -1 7 5 |

I get

|1 -1 0 2 -1 |
| 1 -1 0 2 -1|
|-1 1 -1 7 5 |