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## 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?