Chapter 2.9, Problem 30E

[M] Let H = Span {v₁, v₂, v₃} and B= {v₁, v₂, v₃}.Show that B is a basis for H and x is in H, and find the B-coordinate vector of x, when

v₁ = $\left[\begin{array}{c}\begin{array}{l}-6\\ 4\\ -9\\ 4\end{array}\end{array}\right]$, v₂ = $\left[\begin{array}{c}\begin{array}{l}8\\ -3\\ 7\\ -3\end{array}\end{array}\right]$, v₃ = $\left[\begin{array}{c}\begin{array}{l}-9\\ 5\\ -8\\ 3\end{array}\end{array}\right]$, v₄ = $\left[\begin{array}{c}\begin{array}{l}4\\ 7\\ -8\\ 3\end{array}\end{array}\right]$