 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/a/solution

A c

adds each row. Equating it to

b

α + β + γ = 2, α + 3 β + γ = 4, 2 α + 4 β + 2 γ = 6.

The last equation is the sum of the first two, so it supplies no further restriction. Subtracting the first from the second gives

2 β = 2

, hence

β = 1

, and then

γ = 1 - α

α \in R, β = 1, γ = 1 - α .

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