 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2002/paper-1/8/c/solution

For the specified coordinate vectors,

L = (1011), M = (1 - 1 01) .

Choose the orthogonal matrix representing a quarter-turn,

S = (01 - 1 0) .

Then

S^{T} S = I

S^{T} L S = (1 - 1 01) = M

. Thus these two shear mappings are orthogonally similar.

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