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Volume of Ellipsoid

Source: 2019 South Korea USMC P2

August 13, 2020
Volumecalculuscollege contestslinear algebra

Problem Statement

Matrices AA, BB are given as follows. A=\begin{pmatrix} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix},   B = \begin{pmatrix} 4 & 2 & 0 \\ 2 & 4 & 0 \\ 0 & 0 & 12\end{pmatrix} Find volume of V={x∈R3:x⋅Ax≤1<x⋅Bx}V=\{\mathbf{x}\in\mathbb{R}^3 : \mathbf{x}\cdot A\mathbf{x} \leq 1 < \mathbf{x}\cdot B\mathbf{x} \}.
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