 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/digital-systems-linear-algebra-introduction-to-formal-proof/4/b/solution

The columns are linearly independent. A linear combination of them with coefficients

x_{1}, x_{2}, x_{3}

is exactly

A x

. Part (a) shows that this vanishes only when all three coefficients vanish, which is the definition of column independence. Hence

A

has column rank three.

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