Let \( \left\{\mathbf{u}_{1}=\left[\begin{array}{l}1 \\ 2 \\ 0\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{c}-15 \\ 5 \\ 10\end{array}\right], \mathbf{u}_{3}=\left[\begin{array}{c}3 \\ -4 \\ 4\end{array}\right]\right\} \) be a basis for \( \mathbb{R}^{3} \). Use the Gram-Schmidt process to find an orthogonal basis under the Euclidean inner product. Orthogonal basis: \( \left\{\mathbf{v}_{1}=\left[\begin{array}{l}1 \\ 2 \\ 0\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{c}-14 \\ 7 \\ 10\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{l}a \\ b \\ c\end{array}\right]\right\} \) \( a= \) Ex: \( 1.23: \quad b= \) Ex: \( 1.23 \quad c= \) Ex: 1.23
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