 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-systems-linear-algebra-introduction-to-formal-proof-resit/6/c/solution

The pivot columns are columns 1, 2 and 3 of the original matrix. A basis for its column space is therefore

⎩ ⎨ ⎧ 21101, 21200, 10110 ⎭ ⎬ ⎫ .

Use the original columns, rather than the columns of the row-reduced matrix: elementary row operations preserve column dependence relations, but can change the column space as a subspace of

R^{5}

 New to topics? Read the docs here!