(8%) Let M
2(R) be the vector space of all 2 X 2 matrices with real coefficients and let Pz be the
vector space of all real polynomials of degree at most 2. Define T: M
2(R) → P
2 by
=(a+b)+2dx+bx
2.
Let B=
and C={1,x,x2},D={1+x,x,1+x
2}
Be ordered bases for M
2(R) and P
2, respectively. Determine
【題組】(b) (4%) The matrix representation of T relative to ordered bases B, D.