 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2015-resit/11/c/solution

All three eigenvalues are nonzero, so

D^{- 1} = diag (- 1, 1/2, 1)

. The inverse matrix is therefore

A^{- 1} = B D^{- 1} B^{- 1} = 4 1/2 3 3 1/2 3 - 5 - 1/2 - 4 .

Multiplying this matrix by

A

gives

I

, independently checking both the sign and the fractions.

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