Warner Christensen
09/13/2023 · Middle School
Let \( \left\{\mathbf{u}_{1}=\left[\begin{array}{c}-2 \\ 0\end{array}\right], \mathbf{u}_{2}=\left[\begin{array}{c}-1 \\ 2\end{array}\right]\right\} \) be a basis for \( \mathbb{R}^{2} \). Use the Gram-Schmic basis under the Euclidean inner product. Orthogonal basis: \( \left\{\mathbf{v}_{1}=\left[\begin{array}{c}-2 \\ 0\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{l}a \\ b\end{array}\right]\right\} \) \( a= \) Ex. \( 5 \quad b= \) Ex.5
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The orthogonal basis for \( \mathbb{R}^{2} \) is \( \left\{\mathbf{v}_{1}=\left[\begin{array}{c}-2 \\ 0\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{l}0 \\ 2\end{array}\right]\right\} \).
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