Solved: In 3 and 4, verify that the basis B for the given vector space is orthogonal
Chapter 7, Problem 3(choose chapter or problem)
In Problems 3 and 4, verify that the basis B for the given vector space is orthogonal. Use Theorem 7.7.l as an aid in finding the coordinates of the vector u relative to the basis B. Then write u as a linear combination of the basis vectors.
\(\begin{array}{l} B=\left\{\langle 1,0,1\rangle,\langle 0,1,0\rangle,\langle-1,0,1\rangle, R^{3}\right. \\ \mathbf{u}=\langle 10,7,-13\rangle \end{array} \)
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