Linear transformation with standard basis

[foreverdream]

Homework Statement

Let s be the linear transformation
s: P2→ R^3 ( P2 is polynomial of degree 2 or less)
a+bx→(a,b,a+b)
find the matrix of s and the matrix of tos with respect to the standard basis for the domain
P2 and the standard basis for the codomain R^3

The Attempt at a Solution

Now I know that Standard basis of P2 is {1,x}
and standard basis for R^3 = {(1,0,0), (0,1,0), (0,0,1)}
and s(1)= (1,0,1)
and s(x) = (0,1,1)

but I don't know how to proceed from here?

 

[zooxanthellae]

Well we know s: P2 -> R3 so the map of s will have 2 columns and 3 rows. The first row will be (1, 0). Can you do the rest?

To find the matrix with respect to P2's basis and R3's basis, you proceed by taking a vector in P2, applying s to it, then expressing the result using R3's basis. Repeating this for each vector in P2 gives the matrix. How do these compare?

You might find this helpful: http://www.millersville.edu/~bikenaga/linear-algebra/matrix-linear-trans/matrix-linear-trans.html .

It might be helpful to think of the resultant matrix as a way of "translating" between the languages of P2 and R3.

Hope that helps!

 

[foreverdream]

Thanks. I'll try and post back my findings.

 

[foreverdream]

am I correct?

 

[foreverdream]

still working on it

 

[foreverdream]

trying not suceeded

 

[foreverdream]

i resolved it no help needed