 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/18/b/ii/solution

For the choice of

B

in part (b)(i), the two-by-two matrix inverse formula gives

B^{- 1} = \frac{1}{3} (- 1 2 - 2 1) .

B B^{- 1} = B^{- 1} B = I

, providing a direct check.

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