Chapter 4.4, Problem 1PP

Let ${\text{b}}_1=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$, ${\text{b}}_2=\left[\begin{array}{c}-3\\ 4\\ 0\end{array}\right]$, ${\text{b}}_3=\left[\begin{array}{c}3\\ -6\\ 3\end{array}\right]$, and $\text{x}=\left[\begin{array}{c}-8\\ 2\\ 3\end{array}\right]$.

1. a. Show that the set B = {b₁, b₂, b₃} is a basis of ℝ³.
2. b. Find the change-of-coordinates matrix from B to the standard basis.
3. c. Write the equation that relates x in ℝ³ to [x]_B.
4. d. Find [x]_B, for the x given above.