Lat3 bt2 ct d at3 3a bt2 2b ct cd find the matrix of

L(at³ + bt² + ct + d) = at³ + (3a +b)t² + (2b +c)t + (c+d)

find the matrix of L with respect to S and T

s = ( t³, t²,t,1) and t = (t³+t²,t²+t,t+1,1)

Solution

We have L(at³ + bt² + ct + d) = at³ + (3a +b)t² + (2b +c)t + (c+d). Therefore, the coordinate matrix of L with respect to S = ( t³, t²,t,1) is ( a, 3a+b, 2b +c ,c + d). Also, L(at³ + bt² + ct + d) = at³ + (3a +b)t² + (2b +c)t + (c+d) = a(t³+ t²) + (2a+b)( t²+ t) + ( b + c – 2a)( t+1) + 2a –b + d . Therefore, the coordinate matrix of L with respect to T =(t³+t²,t²+t,t+1,1) is ( a, 2a + b, b + c – 2a, 2a –b + d)