Let \( \left\{U_{1}=\left[\begin{array}{ll}1 & 0 \\ 0 & 2\end{array}\right], U_{2}=\left[\begin{array}{cc}0 & 10 \\ 5 & 0\end{array}\right], U_{3}=\left[\begin{array}{cc}-3 & 0 \\ 0 & -2\end{array}\right]\right\} \) be a basis for a subspace of \( \mathbb{R}_{2 \times 2} \). Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: \( \left\{V_{1}=\left[\begin{array}{ll}1 & 0 \\ 0 & 2\end{array}\right], V_{2}=\left[\begin{array}{cc}a & 10 \\ b & 0\end{array}\right], V_{3}=\left[\begin{array}{cc}-1.6 & c \\ 0 & d\end{array}\right]\right\} \) \( a= \) Ex:5 \( \quad b= \) Ex: \( 5 \quad c= \) Ex: \( 1.23 \quad d= \) Ex: 1.23
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