MathDB

2

Part of 2019 Korea USCM

Problems(1)

Volume of Ellipsoid

Source: 2019 South Korea USMC P2

8/13/2020
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} \}.
Volumecalculuscollege contestslinear algebra