Solved: In 912, use the GramSchmidt orthogonalization process (4) to transform the given
Chapter 7, Problem 11(choose chapter or problem)
In Problems 9-12, use the Gram-Schmidt orthogonalization process (4) to transform the given basis \(B=\left\{\mathbf{u}_{1}, \mathbf{u}_{2}, \mathbf{u}_{3}\right\} \text { for } R^{3}\) into an orthogonal basis \(B^{\prime}=\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}\). Then form an orthonormal basis \(B^{\prime \prime}=\left\{\mathbf{w}_{1}, \mathbf{w}_{2}, \mathbf{w}_{3}\right\}\).
\(B=\left\{\left\langle\frac{1}{2}, \frac{1}{2}, 1\right\rangle,\left\langle-1,1,-\frac{1}{2}\right\rangle,\left\langle-1, \frac{1}{2}, 1\right\rangle\right\}\)
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