Chapter 4.3, Problem 36E

[M] Let H = Span {u₁, u₂, u₃} and K = Span{v₁,v₂, v₃}, where

${\text{u}}_1=\left[\begin{array}{c}1\\ 2\\ 0\\ -1\end{array}\right]$, ${\text{u}}_2=\left[\begin{array}{c}0\\ 2\\ -1\\ 1\end{array}\right]$, ${\text{u}}_3=\left[\begin{array}{c}3\\ 4\\ 1\\ -4\end{array}\right]$

${\text{v}}_1=\left[\begin{array}{c}-2\\ -2\\ -1\\ 3\end{array}\right]$, ${\text{v}}_2=\left[\begin{array}{c}2\\ 3\\ 2\\ -6\end{array}\right]$, ${\text{v}}_3=\left[\begin{array}{c}-2\\ -2\\ -1\\ 3\end{array}\right]$

Find bases for H, K, and H + K. (See Exercises 33 and 34 in Section 4.1.)