Solved: In 1 and 2, verify that the basis B for the given vector space is orthonormal
Chapter 7, Problem 2(choose chapter or problem)
In Problems 1and 2, verify that the basis B for the given vector space is orthonormal. Use Theorem 7.7.1 to find the coordinates of the vector u relative to the basis B. Then write u as a linear combination of the basis vectors.
\(\begin{array}{l} B=\left\{\left\langle\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}\right\rangle,\left\langle 0,-\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right\rangle\right. \\ \left.\left\langle-\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}},-\frac{1}{\sqrt{6}}\right\rangle\right\}, \quad R^{3} ; \quad \mathbf{u}=\langle 5,-1,6\rangle \end{array} \)
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