Prove that for a diagonalisable square matrix A, the determinant is the product of the eigenvalues of A matrix and the trace is the sum of the eigenvalues of A. You may use that the trace is cyclic, that is, Tr(ABC) = Tr(CAB) = Tr(BCA), for any 3 square matrices A, B, C of the same size.
Prove that for a diagonalisable square matrix A, the determinant is the product of the eigenvalues of A matrix and the trace is the sum of the eigenvalues of A. You may use that the trace is cyclic, that is, Tr(ABC) = Tr(CAB) = Tr(BCA), for any 3 square matrices A, B, C of the same size.
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 4SE: Can a matrix with an entire column of zeros have an inverse? Explain why or why not.
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Prove that for a diagonalisable square matrix A, the determinant is the product of
the eigenvalues of A matrix and the trace is the sum of the eigenvalues of A. You
may use that the trace is cyclic, that is, Tr(ABC) = Tr(CAB) = Tr(BCA), for
any 3 square matrices A, B, C of the same size.
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