Finding a basis for the range space

[Janiceleong26]

1. Homework Statement

I've found the dimension of V to be 3.
According to the solutions, it seems that the basis can be written straight away, { (1,1,1,2), (1,2,-3,1), (3,4,-1,5) } (which is also the basis for the column space of the matrix), without verifying the vectors are linearly independent.. how come? The vectors in the matrix are not necessary linearly independent..

 

[mfb]

Those three vectors cannot be a basis of anything, because they are linearly dependent. You can choose any three other columns to get an independent set.

 

[Janiceleong26]

Those three vectors cannot be a basis of anything, because they are linearly dependent. You can choose any three other columns to get an independent set.

Oh right.. I know how to do already, thanks!