 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/e/solution

Using the ordered orthonormal basis chosen in (c), the column matrix is

B = 1/ 2 0 1/ 2 1/ 2 0 - 1/ 2 010 .

Other signs or another orthonormal choice within the repeated eigenspace are equally valid, provided the same choice is retained in the remaining parts.

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