Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Digital systems, linear algebra, introduction to formal proof / 4 / b / i / Solution

Gaussian elimination givesElementary row operations preserve the row space, so $\{(1,0,1),(0,1,2)\}$ is a basis. The two rows are linearly independent because their first two coordinates form the standard basis of ${\mathbb{R}}^2$.