 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/18/b/solution

Substituting

β = 1

and

γ = 1 - α

into the matrix gives

A_{α} = α + 1 2 2 - α 1 - α α α + 3 2 2 - α 1 .

Its row sums are

4, 4, 6

, checking that

A_{α} c = b

for every real

α

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