 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/digital-systems-linear-algebra-introduction-to-formal-proof/6/a/ii/solution

For eigenvalue zero take

s_{1} = (1, 0)^{T}

3/8

, the first row of

(B - 3 I /8) s_{2} = 0

gives

x = - 2 y

, so take

s_{2} = (- 2, 1)^{T}

S = (10 - 2 1), S^{- 1} = (1021), D = (00 0 3/8) .

The identities

B s_{i} = λ_{i} s_{i}

give

BS = S D

, hence the required diagonalization

S^{- 1} BS = D

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