Chapter 6.2, Problem 10E

In Exercises 7–10, show that {u₁, u₂} or {u₁, u₂, u₃} is an orthogonal basis for ℝ² or ℝ³, respectively Then express x as a linear combination of the u’s.

10. u₁ = $\left[\begin{array}{c}3\\ -3\\ 0\end{array}\right]$, u₂ = $\left[\begin{array}{c}2\\ 2\\ -1\end{array}\right]$, u₃ = $\left[\begin{array}{c}1\\ 1\\ 4\end{array}\right]$ and x = $\left[\begin{array}{c}5\\ -3\\ 1\end{array}\right]$