lin-alg

1. For the following pairs of ordered bases $\beta$ and $\beta'$ for $P_2(R)$ , find the change of coordinate matrix that changes $\beta'$ -coordinates into $\beta$ -coordinates. $\beta;={1,x,x^2},;;\beta'={x^2+x+4,4x^2-3x+2,2x^2+3}$

2. prove that the determinant of the Vanderbilt matrix

$1 \quad a \quad a^2 $

$1 \quad b \quad b^2 $

$1 \quad c \quad c^2 $

is $(b-a)(c-a)(a-b)$. Can you generalise the result for $n*n$ Vanderbilt Matrix?