Matrix associated to eigenspaces

[cdub2]

Homework Statement

Find a 2 x 2 matrix A for which:
E2 = span (-3, 5)
E1 = span (1, -2)
where E is the eigenspace associated with each eigenvalue.

Homework Equations

The Attempt at a Solution

I know that to find the eigenspace from the matrix A I would use the equation
E2 = ker (2(Identity) - A) but I can't figure out how to go backwards from the eigenspaces to the matrix A.

 

[Dick]

All you need to define a 2x2 matrix is the value of A(v1) and A(v2) for any two linearly independent vectors v1 and v2. Can you start applying that to your problem?