\( \text{The set of } x \in \mathbb{R}^3 \text{ for which } \displaystyle\max_{\!\!-1 \le t \le 1} x^T P(t) x \le 1 \)
\( \text{Click on a matrix below to select a matrix } P(t) \)
\( \begin{bmatrix} 6{-}4t & 2{-}3t & 1{-}t \\ 2{-}3t & 3{-}t & -t \\ 1{-}t & -t & 2 \end{bmatrix} \)
\( \begin{bmatrix} 4{-}t^2 & t{+}1 & 2{-}t^2 \\ t{+}1 & 2t^2{+}t{+}2 & t^2{-}t{+}1 \\ 2{-}t^2 & t^2{-}t{+}1 & 2t^2{+}2t{+}4 \end{bmatrix} \)
\( \begin{bmatrix} 1 & t & 0 \\ t & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \)
\( \begin{bmatrix} 4t{+}8 & {-}3t{-}1 & 0 \\ {-}3t{-}1 & {-}4t{+}12 & 0 \\ 0 & 0 & 1 \end{bmatrix} \)
\( \begin{bmatrix} 2{-}t^2 & t & 0 \\ t & 3{-}t^2 & 0 \\ 0 & 0 & 1 \end{bmatrix} \)