Given $T: P_2 \rightarrow P_3$ defined by:
$T(at^2 + bt +c) = (a-b+c)t^3 + (-a + 3b - 2c)t^2 +(-a-b)t +(2b-c)$
What is the corresponding Matrix of $T$?
This is what I have: First I rewrite the transformation as follows:
$T_0 = 2b - c$
$T_1 = -a - b$
$T_2 = -a + 3b -2c$
$T_3 = a-b+c$
And I know $T_i = \sum \limits_{j=1}^n \mu_{ji} b_i$ where $b_i$ is the basis vector.
So my matrix $\mu$ is $\pmatrix{0&-1&-1&1\\ 2&-1&3&-1\\ -1&0&-2&1}$
- Is this correct?
- Is my rewriting of $T$ correct?