Answer to Question #44405 in Linear Algebra for Vincent

Let B1={[1 1], [1 0], [1 0] and B2={[1 0], [0 1], [0 1]
[0 1] [0 1] [0 -1] } [0 0] [0 1] [0 -1] }
be 2 bases for span(B1) in M22, with the usual left to right ordering.
Let B3 be a basis for P1 and be the transition matrix from B2 to B3 giiven by [1 1 1]
[0 1 1] = PB2→B3
[0 0 1]
a) Find transition matrix PB1→B3
b) Use PB2→B3 to find B3