 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2014/12/ii/solution

An explicit basis is

E_{1} = (1000), E_{2} = (0001), E_{3} = (0110) .

Indeed every real symmetric matrix

(a b b c)

a E_{1} + c E_{2} + b E_{3}

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