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(a) (15 pts) What must be the k if the matrix egin{bmatrix} 3 & -1 & 1 \ 0 & 2 & k \ 0 & 1 & -1 end{bmatrix} has three distinct real eigenvalues.

          (a) (15 pts) What must be the k if the matrix egin{bmatrix} 3 & -1 & 1 \ 0 & 2 & k \ 0 & 1 & -1 end{bmatrix} has three distinct real eigenvalues.

Added by Dana B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Nicole Hoffman

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The characteristic polynomial of a matrix \( A \) is given by \( \det(A - \lambda I) \), where \( \lambda \) is an eigenvalue and \( I \) is the identity matrix. For the given matrix \( A = \begin{bmatrix} 3 & -1 & 1 \\ 0 & 2 & k \\ 0 & 1 & -1 \end{bmatrix} \), we Show more…

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What must be the if the matrix a 5] has three distinct real eigenvalues? The trace of matrix A is 011 + 022, which can be calculated by the summation of all eigenvalues, and the determinant can be calculated by the product of all eigenvalues. Let Î»1, Î»2, and Î»3 be the eigenvalues of A. What is the determinant of (A-1)T? Let A = [a b; c d]. A. (3 pts) If trace(A) = 10 for Î»i = 5, find A. B. (3 pts) By using the result of (i), find det(A). C. (3 pts) Determine one matrix A that satisfies parts (i) and (ii).