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Image/Column space of a Matrix

Hey there!

I'm really struggling with this question :(. The solutions on it don't seem to match up with everything i've read/googled!

Now, I understand how to get the kernel. But I have no idea what they are doing to get the image basis!

I've looked around on wikipedia etc and read that you take the corresponding columns to the pivots - which to me would mean the basis would be: (1 0 3), (-2, 2, -4)...Not (1; 2; 1); (2; 0; 6)

Please see the pdf attachment for the solutions.

Any help would be appreciated!

Thankyou!

Re: Image/Column space of a Matrix