1. The problem statement, all variables and given/known data Determine if the matrix is diagonalizable. If so, find matrices S and (symbol that looks simlar to A) such that the given matrix equals S(weird symbol)S^(-1). 2. Relevant equations C1X1+C2X2+....CnXn = 0 3. The attempt at a solution So what I did was take the matrix | 1 4 | and transform it to | λ-1 -4| | 1 -2 | | -1 λ+2| Then I said (λ-1)(λ+2)-4 which equals λ^2+λ-6 I found that the eigenvalues were -3 and 2 whic I then took and plugged -3 into the matrix equation that I transformed with the lamdas. Then I did this | -4 -4 | | x1 | |0| | -1 -1 | | x2 | = |0| which gave me two equations -4x1-4x2 = 0 and -x1-x2 = 0 but this is where im lost which one should I assign an abritray variavle to x1 or x2 I get that it is only to none pivot numbers and the second row are constants so you cant use those but I have seen in some cases where that is not true so im confused? Anyways solve that and I get v1 = |1 | |-1| and then I use the same procedure with the other eigen val and get v2 = |4| |1| I put those together and achieve | 1 4 | |-1 1 | this is incorrect however it is supposed to be | 4 1 | | 1 -1 | why is this and how do I know which eigenvalue gives me which eigenvector?