Image of Linear Transformation

[Jfhebb]

Hi, the question is for the transformation :
T: M2,3 -> P2
T ( A11 A12 A13) = (A11 + A13)x^2 + (A21 - A22)x + A23
( A21 A22 A23)

Are the following in the linear transformation?
W1=x^2 + 2x + 1
W2=x-2

Attempt: I figured that w would be in image if there exists..
(A11 + A13)x^2 + (A21 - A22)x + A23= C2x^2 + C1x + C0

I am not quite sure where to go from here, any help is appreciated

 

[Stephen Tashi]

For W1, you can set up simultaneous equations:
A11 + A13 = 1
A21 + A22 = 2
A23 = 1
and see what the theory of simultaneous equations tells you.

I don't think you are stating the question precisely. If this is a textbook question, you should ask it in the section of the forum that is designated for homework questions and you should quote the problem exactly.