In 5 - 8, use the GramSchmidt orthogonalization process (3) to transform the given basis
Chapter 7, Problem 6(choose chapter or problem)
In Problems 5-8, use the Gram-Schmidt orthogonalization process (3) to transform the given basis \(B=\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\} \text { for } R^{2}\) into an orthogonal basis \(B^{\prime}=\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}\). Then form an orthonormal basis \(B^{\prime \prime}=\left\{\mathbf{w}_{1}, \mathbf{w}_{2}\right\}\).
(a) First construct B" using \(\mathbf{v}_{1}, \mathbf{u}_{1}\).
(b) Then construct B" using \(\mathbf{v}_{1}, \mathbf{u}_{1}\).
(c) Sketch B and each basis B".
\(B=\{\langle-3,4\rangle,\langle-1,0\rangle\}\)
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