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**Find a 2\times 2 matrix A for which**

E_4 = span [1,-1] and E_2 = span [-5, 6]

where E_(lambda) is the eigenspace associated with the eigenvalue (lambda)

E_4 = span [1,-1] and E_2 = span [-5, 6]

where E_(lambda) is the eigenspace associated with the eigenvalue (lambda)

**relevant equations: Av=(lambda)v**

**3. The Attempt at a Solution**

I've pretty much gotten most of the eigenspace/value problems down, but this one I'm clueless on how to work. Seems that you would have to work backwards , but I don't know how to do that.