Linear Transformations: Linear Transformation from P2 to R3 Given the Range ONLY!!

We are going to learn how to find the linear transformation of a polynomial of order 2 (P2) to R3 given the Range (image) of the linear transformation only. First, we need to find a set of vectors for the range and since we need to associate this base to the starting point (P2), we find the linear transformation fot T(1), for T(x) and for T(X^2), this last transformation will be vector (0,0,0) since there are only 2 vectors on the base of the range. Once we find this, we turn the polynomial into a linear combination to find the coefficients a, b and c for polynomials a+bx+cx^2 and since last vector is (0,0,0), we will not have other value for C different from Zero (0).

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