Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics and probability resit / 5 / c / i / Solution

Put $q(x)=x^{T}Ax$ and $t(x)=x^{T}b$. The product rule givesDifferentiate each term. The derivative of $2tAx$ is $2(Ax)b^T+2tA$, while that of $qb$ is $2b(Ax{)}^T$. HenceThe last two terms are transposes of each other, so this Hessian matrix is symmetric, as expected.