- #1
says
- 594
- 12
Homework Statement
f: p2 to R2, f(ax2+bx+c) = (a+b, b+c) = V12. Homework Equations
Create a p2 to R2 polynom and R2 equation that is equivalent to the above statement, so:
f(dx2+ex+g) = (d+e, e+g) = V2
Therefore a=d b=e c=g
f(ax2+bx+c) = (a+b, b+c) = f(dx2+ex+g) = (d+e, e+g)
The Attempt at a Solution
T(V1+V2) = T(V1) + T(V2)
T(V1+V2) = T(V1) +T(V2) for a linear transformation
T(V1+V2) =T(a+d, b+e) + (b+e, c+g) = T(a+d+b+e, b+e+c+g)
T(V1) + T(V2) = (a+b, b+c) + (d+e, e+g) = T(a+b+d+e, b+c+e+g)
T(a+d+b+e, b+e+c+g) = T(a+b+d+e, b+c+e+g) FIRST CONDITION MET!
T(wV1) = Tw(V1)
T(w(a+b,b+c) = Tw(a+b,b+c)
T(wa+wb, wb+wc) = (Twa+Twb, Twb +Twc)
(Twa+Twb, Twb +Twc) = (Twa+Twb, Twb +Twc) SECOND CONDITION MET!
This is a linear transformation from p2 to R2.
I was hoping someone could help me out just to make sure I'm on the right track. I get a bit confused with vectors and column vector notation in linear algebra.