 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/e/solution

x_{p} = (1, 0, - 1, 0)^{T}

, as direct substitution into all five equations verifies. Add any vector in the null space to obtain every solution:

x = 10 - 1 0 + t - 1 1 - 1 1, t \in R .

Conversely, the difference of any two solutions is annihilated by

A

, so there are no further solutions. This is the affine solution space of a consistent linear system.

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