 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/11/f/solution

The

(i, j)

entry of

B^{T} B

e_{i} \cdot e_{j} = δ_{ij}

. Hence

B

B^{- 1} = B^{T} = 1/ 2 1/ 2 0 001 1/ 2 - 1/ 2 0 .

This obtains the inverse without unnecessary cofactor calculations.

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