 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/5/e/solution

A^{T} = - A

. By parts (c) and (d),

det (A) = det (A^{T}) = det (- A) = (- 1)^{n} det (A) .

n

is odd,

det (A) = - det (A)

, hence

2 det (A) = 0

over

R

. Therefore $det (A) = 0$ , so $A$ is a singular matrix. The conclusion depends on odd dimension: in dimension two,

(0 - 1 10)

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