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 Nov6 awarded Notable Question Nov22 awarded Popular Question Oct16 asked Linear independent sets of non-square matricies Oct15 awarded Student Oct14 awarded Scholar Oct14 accepted Finding multiple linearly independent eigenvalues for a single eigenvalues Oct13 awarded Editor Oct13 revised Finding multiple linearly independent eigenvalues for a single eigenvalues fix math typo, spelling Oct13 comment Finding multiple linearly independent eigenvalues for a single eigenvalues Ok, I think I get it. So you just use any two values for $x_2, x_3$ that produces something easy to work with, and make sure they are linearly independent. Would $x_2 = 2, x_3 = 1$ therefore $e_1$ = (-2, 2, 1) and $x_2 = 0, x_3 = 1$ therefore $e_2$ = (-1, 0, 1) be a valid answer? I've had the same problem in another question, so using this would (1,1,0) and (0,1,0) be ok for {{1,1/2,-1/2},{1/2,1,1/2},{-1/2,1/2,1}}? Oct13 asked Finding multiple linearly independent eigenvalues for a single eigenvalues Oct13 awarded Autobiographer