Let B = {3 + 2x + x² , 1 + x + 2x² , 1 + 2x} and B^' = {1 + x x² , x + 2x² ,1 + 4x}

be two non-standard bases for P₂(x). Let p₁ = 1 + x + x² P₂(x).

Calculate [p₁]_B and [p₁]_B'

Use the change of basis matrix.