 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/17/c/solution

K y_{0} = f_{0}

K

are nonzero, so it is invertible and

y_{0} = K^{- 1} f_{0}, K^{- 1} = \frac{1}{4} 310130001 .

For the specified constant source this gives

y_{0} = (1, 1, 1/4)^{T} .

Indeed the first two rows of

K y_{0}

each give one, and the third gives

4 (1/4) = 1

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