I am doing some practice questions and I'm not too sure where to start on this one:
- Consider the bases $B = \{p_1,p_2\}$ and $B' = \{q_1,q_2\}$ of P$_1$, the polynomials of degree $\le$ 1, where $p_1 = 2$; $p_2 = x - 1$; $q_1 = x + 3$; $q_2 = x + 1.$
(a) Find the transition matrix from B' to B.
(b) Find the transition matrix from B to B'.
(c) Let $p = 2x - 1$. Compute $[p]_B$, the coordinates of $p$ with respect to $B$, and then use (b) to find $[p]_{B'}$, the coordinates of $p$ with respect to $B'$.
Any help is appreciated.