 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/d/solution

The reduced homogeneous system is

x_{1} + x_{4} = 0

x_{2} - x_{4} = 0

x_{3} + x_{4} = 0

x_{4} = t

to obtain

ker A = span ⎩ ⎨ ⎧ - 1 1 - 1 1 ⎭ ⎬ ⎫, dim ker A = 1.

3 + 1 = 4

, and substitution verifies that the displayed vector is annihilated by

A

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