What Is the Impact of Mapping in Linear Transformations from P2 to P3?

[Pouyan]

Homework Statement

Let T: P2 --> P3 be the transformation that maps a polynomial p(t) into the polynomial (t+5)p(t).

a) find the image of p(t)= 2-t+(t^2)
b) Find the matrix for T relative to bases {1,t,t^2} and {1,t,t^2,t^3}.

Homework Equations

Given

The Attempt at a Solution

a) I know (t+5)p(t)=(t+5)(2-t+(t^2))= 10-3t+4(t^2)+(t^3)

b) I see in solution T(1) = (t+5) (1)= t+5
T(t) = (t+5)(t)
T(t^2)=(t+5)(t^2)
and so on ...

My question is why T(1)= 1 and T(t) = t ?! I see that T(1) means p(t)=1 or T(t)=p(t)=t but why is this so ?!

 

[vela]

Homework Statement

Let T: P2 --> P3 be the transformation that maps a polynomial p(t) into the polynomial (t+5)p(t).

a) find the image of p(t)= 2-t+(t^2)
b) Find the matrix for T relative to bases {1,t,t^2} and {1,t,t^2,t^3}.

Homework Equations

Given

The Attempt at a Solution

a) I know (t+5)p(t)=(t+5)(2-t+(t^2))= 10-3t+4(t^2)+(t^3)

b) I see in solution T(1) = (t+5) (1)= t+5
T(t) = (t+5)(t)
T(t^2)=(t+5)(t^2)
and so on ...

My question is why T(1)= 1 and T(t) = t ?! I see that T(1) means p(t)=1 or T(t)=p(t)=t but why is this so ?!

T(1) isn't equal to 1, nor is T(t) equal to t. Why do you think they are?

 

[Pouyan]

T(1) isn't equal to 1, nor is T(t) equal to t. Why do you think they are?

I see in my solution B={1,t,t^2} and C={1,t,t^2,t^3} Since T(b1)=T(1)=(t+5)(1)=t+5, [T(b1)] relative to C =[5,1,0,0,]