Chapter 5.1, Problem 10EQ

In Exercises 7-10, show that the given vectors form an orthogonal basis for ${ℝ}^{2}or{ℝ}^3$. Then use Theorem 5.2 to express was a linear combination of these basis vectors. Give the coordinate vector $\left[\text{w}\right]\beta$ ofwwith respect to the basis $\beta =\left\{{\text{v}}_{\text{1}}{\text{, v}}_{\text{2}}\right\}$of ${ℝ}^2$or $\beta ={\text{v}}_{\text{1}}{\text{,v}}_{\text{2}}{\text{, v}}_{\text{3}}$ of ${ℝ}^3$.

${\text{v}}_1=\left[\begin{array}{l}1\\ 1\\ 1\end{array}\right],{\text{v}}_2=\left[\begin{array}{l}1\\ -1\\ 0\end{array}\right],{\text{v}}_3=\left[\begin{array}{l}1\\ 1\\ -2\end{array}\right];\text{w}=\left[\begin{array}{l}1\\ 2\\ 3\end{array}\right]$