 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/9/solution

Expanding the quadratic form gives

(x y) (1 a_{21} 4 a_{22}) (y x) = x^{2} + (4 + a_{21}) x y + a_{22} y^{2} .

Matching coefficients of

x y

and

y^{2}

yields

a_{21} = 4, a_{22} = 4 .

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