Chapter 6.3, Problem 1E

In Exercises 1 and 2, you may assume that {u₁,…, u₄} is an orthogonal basis for ℝ⁴.

1. u_{1 =} $\left[\begin{array}{c}0\\ 1\\ -4\\ -1\end{array}\right]$, u_{2 =} $\left[\begin{array}{c}3\\ 5\\ 1\\ 1\end{array}\right]$, u_{3 =} $\left[\begin{array}{c}1\\ 0\\ 1\\ -4\end{array}\right]$, u_{4 =} $\left[\begin{array}{c}5\\ -3\\ -1\\ 1\end{array}\right]$, x = $\left[\begin{array}{c}10\\ -8\\ 2\\ 0\end{array}\right]$

Write x as the sum of two vectors, one in Span {u₁, u₂, u₃} and the other in Span {u₄}.