Let $\mathbf{S}=\left(\begin{array}{cccc}1 & 0 & -1 & -2 \ 2 & 1 & 0 & 1 \ 0 & -1 & 2 & -1 \ -1 & 0 & 3 & 2\end{array}\right), \vec{u}=(-3,1,-1,0)$, and $\vec{v}=(1,2,0,-3)$. What is $\mathbf{S} \vec{u} \cdot \mathbf{S} \vec{v}$ ?

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The Answer of Let $\mathbf{S}=\left(\begin{array}{cccc}1 & 0 & -1 & -2 \ 2 & 1 & 0 & 1 \ 0 & -1 & 2 & -1 \ -1 & 0 & 3 & 2\end{array}\right), \vec{u}=(-3,1,-1,0)$, and $\vec{v}=(1,2,0,-3)$. What is $\mathbf{S} \vec{u} \cdot \mathbf{S} \vec{v}$ ?

Let S=(10−1−221010−12−1−1032),u⃗=(−3,1,−1,0)\mathbf{S}=\left(\begin{array}{cccc}1 & 0 & -1 & -2 \\ 2 & 1 & 0 & 1 \\ 0 & -1 & 2 & -1 \\ -1 & 0 & 3 & 2\end{array}\right), \vec{u}=(-3,1,-1,0)S=​120−1​01−10​−1023​−21−12​​,u=(−3,1,−1,0)

Let $\mathbf{S}=\left(\begin{array}{cccc}1 & 0 & -1 & -2 \\ 2 & 1 & 0 & 1 \\ 0 & -1 & 2 & -1 \\ -1 & 0 & 3 & 2\end{array}\right), \vec{u}=(-3,1,-1,0)$