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## Homework Statement

Construct an isomorphism from a 2 by 2 symmetric matrix to R^3.

## Homework Equations

N/A

## The Attempt at a Solution

I know that for a transformation to be an isomorphic, it must be one-to-one and onto. Would the transform be T:A->R^3 and I would have to choose a general matrix A to test?

How would I test it not knowing how the transform is mapped?