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 P: 94 1. The problem statement, all variables and given/known data For the following matrix, find the value of t, if any, so that the following matrix is diagonalizable $$A= \begin{pmatrix} 5 & -2 & 4\\ 0 & 3 & t\\ 0 & 0 & 5 \end{pmatrix}$$ 3. The attempt at a solution In order for A to be diagonalizable, we need 3 linearly independent eigenvectors, that is, 3 linearly independent eigenvalues $$det(A-xI)=det \begin{pmatrix} 5-x & -2 & 4\\ 0 & 3-x & t\\ 0 & 0 & 5-x \end{pmatrix}$$ $$=(5-x)det \begin{pmatrix} 3-x & t\\ 0 & 5-x \end{pmatrix}$$ $$= (5-x)((3-x)(5-x)-0t)$$ The eigenvalues are 3 and 5. Obviously, it doesn't matter what t is, we will not be able to get the matrix A to be diagonalizable. My professor said that he thought there was one correct value for t (but he wasn't sure). Is what I've done correct?