Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof / 2 / c

The pivot columns in the row echelon form are columns 1 and 3. Use those columns of the original matrix for a basis of the original column space:For a direct spanning check, column 2 is twice column 1 and column 4 is $(17/5)$ times column 1 minus $(3/5)$ times column 3. The displayed columns are linearly independent, since the first two coordinates of $\alpha c_1+\beta c_3=0$ give $\alpha -\beta =0$ and $\alpha +4\beta =0$, so $\alpha =\beta =0$.