Linear transformation defined by T(a + bx) = (a, a+b)

jeff1evesque
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Example
Let T: P_1(R) --> R^2 be the linear transformation defined by T(a + bx) = (a, a+b).
The reader can verify directly that T-1: R^2 --> P_1(R) is defined by T-1(c, d) = c + (d-c)x. Observe that T-1 is also linear.

I am reading my text and it kind of makes sense, but I have no clue how to verify what has been said above. It make sense to reverse everything, and because after the reversal since the inverse doesn't have the element c for the second element in the order pair for R^2 then we subtract it from the image of T-1? But I don't feel comfortable with the concept (of this reversal-and subtraction), and I don't know how to verify what has been said.
 
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If (c, d) is an element of the range of T (and thus the domain of T-1), then c = a and d = a+b for some element (a + bx) in the domain of T. This should start you in the right direction.
 


slider142 said:
If (c, d) is an element of the range of T (and thus the domain of T-1), then c = a and d = a+b for some element (a + bx) in the domain of T. This should start you in the right direction.

Thank you,

JL
 

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