Let T: ℝ² → P² a linear transformation with usual operations such as
T [1 1] = 1 - 2x and
T [3 -1]= x+2x²
Find T [-7 9] and T [a b]
**Though I'm writing them here as 1x 2 row vectors , all T's are actually 2x1 column vectors (I didn't see a way to give them proper format)**
The Attempt at a Solution
Finding the transformation for the required vectors is not an issue, as long as I have the associated standard matrix, however my approaches to find this matrix have not come out successful.
Since the transformation goes ℝ² → P² it is my understanding that the associated matrix is 3x2 so using the inverse or the transformations of the canonical vectors T(ei) don't seem to help much (or I am failing to see how to properly apply them). The other option it is that this is a linear transformation that is not matricial, in which case I'm uncertain on how to approach it.
Any advise would be appreciated.