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6 Nov 2019
Suppose that A is a nonzero 2 times 2 matrix such that T_A compositefunction T_A = 0. Show that there exists an invertible matrix P such that PAP^-1 = (0 0 1 0). Show that any triangular matrix with distinct diagonal entries is diagonalizable. Find a triangular matrix that is not diagonalizable. Suppose that T: V rightarrow V is a linear operator where V is n-dimensional. If ker(T) is (n - 1)-dimensional and T has a nonzero eigenvalue, show that T is diagonalizable. Show transcribed image text
Suppose that A is a nonzero 2 times 2 matrix such that T_A compositefunction T_A = 0. Show that there exists an invertible matrix P such that PAP^-1 = (0 0 1 0). Show that any triangular matrix with distinct diagonal entries is diagonalizable. Find a triangular matrix that is not diagonalizable. Suppose that T: V rightarrow V is a linear operator where V is n-dimensional. If ker(T) is (n - 1)-dimensional and T has a nonzero eigenvalue, show that T is diagonalizable.
Show transcribed image text Casey DurganLv2
7 May 2019