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## Homework Statement

We're looking at a mapping from P

^{2}(polynomials of degree two or less) to M

^{2}(R) (the set of 2x2 real matrices). The nuance here is that the transformation into the matricies is such that its basis consists of only three independent matrices, making its dimension 3. This means that our transformation maps from P2 (dim = 3) to M2(r) (dim = 3 in this case)

Can a mapping to a subspace make the transformation an isomorphism?