 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/5/d/solution

Q (c) = i, j \sum c_{i} c_{j} x_{i}^{T} x_{j} = (i \sum c_{i} x_{i})^{T} (j \sum c_{j} x_{j}) = i \sum c_{i} x_{i}^{2} .

For

c \neq = 0

\sum_{i} c_{i} x_{i} \neq = 0

, so its squared Euclidean norm is strictly positive. Thus

Q (c) > 0 for every c \neq = 0,

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