 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/12/b/ii/solution

A real two-dimensional antisymmetric matrix has the form

A = (0 - s s 0)

s^{2} = 1/4

, and the specified positive upper-right entry selects

s = 1/2

. Thus

A = (0 - 1/2 1/2 0) .

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