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## Homework Statement

I was given

| 1 2 -1 2 |

| 2 4 1 -2 | = A

| 3 6 0 -6 |

and reduce it to rref.

Also I had to find all four fundamental subspaces of A.

**2. The attempt at a solution**

so I did

R2 - 2R1

R3 - 3R1

R3 - R2

and got

| 1 2 -1 2 |

| 0 0 3 -6 |

| 0 0 0 -6 |

... Arent rref suppose to have all zero row at the bottom? I don't think this is rref because of that -6 in row 3...

and I'm not very sure about how to go about four fundamental subspaces. Am I suppose to solve for C(A), N(A), C(A^T), N(A^T)? and am I suppose to solve for dim for each of them or special solutions?

thank you for replies in adavance