 Solution

ID: 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-resit/6/c/solution

Let

c_{1}, \dots, c_{4}

be the original columns. The first three are linearly independent: restricting them to rows 2, 3 and 4 gives the triangular matrix

100110011,

whose determinant is one. Also

c_{4} = c_{1} - c_{2} + c_{3}

B_{col} = ⎩ ⎨ ⎧ 11001, 11100, 10110 ⎭ ⎬ ⎫ .

These are columns of the original matrix. Taking columns of its reduced row echelon form would generally give the wrong column space.

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