Let $$ \left\{U_{1}=\left[\begin{array}{cc}-2 & 0 \ 0 & 1\end{array} ight], U_{2}=\left[\begin{array}{cc}0 & -10 \ 0 & 0\end{array} ight], U_{3}=\left[\begin{array}{cc}0 & 2 \ 0 & -1\end{array} ight] ight\} $$ be a basis for a subspace of $$ \mathbb{R}_{2 imes 2} $$. Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basic: $$ \left\{V_{1}=\left[\begin{array}{cc}-2 & 0 \ 0 & 1\end{array} ight], V_{2}=\left[\begin{array}{cc}a & -10 \ b & 0\end{array} ight], V_{3}=\left[\begin{array}{cc}-0.4 & c \ 0 & d\end{array} ight] ight\} $$ $$ a= $$ Ex.5 $$ 7 \quad b= $$ Ex.5 $$ \quad c= $$ Ex:1.23 $$ \quad d= $$ Ex. 1.23

Question

Let $$ \left\{U_{1}=\left[\begin{array}{cc}-2 & 0 \ 0 & 1\end{array}ight], U_{2}=\left[\begin{array}{cc}0 & -10 \ 0 & 0\end{array}ight], U_{3}=\left[\begin{array}{cc}0 & 2 \ 0 & -1\end{array}ight]ight\} $$ be a basis for a subspace of $$ \mathbb{R}_{2 	imes 2} $$. Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basic: $$ \left\{V_{1}=\left[\begin{array}{cc}-2 & 0 \ 0 & 1\end{array}ight], V_{2}=\left[\begin{array}{cc}a & -10 \ b & 0\end{array}ight], V_{3}=\left[\begin{array}{cc}-0.4 & c \ 0 & d\end{array}ight]ight\} $$ $$ a= $$ Ex.5 $$ 7 \quad b= $$ Ex.5 $$ \quad c= $$ Ex:1.23 $$ \quad d= $$ Ex. 1.23

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The values of $$ a, b, c, d $$ are $$ a = 0, b = 0, c = 2, d = -1 $$.

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