Problem 1 1.1 If A is an n x n matrix, prove that if A has...

Problem 1

1.1 If A is an n x n matrix, prove that if A has n linearly independent eigenvalues, then A^T is diagonalizable.

1.2 Diagonalize the matrix below with eigenvalues equal to -1 and 5.

0	1	1
2	1	2
3	3	2

1.3 Assume that A is 4 x 4 and has three different eigenvalues, if one of the eigenspaces is dimension 1 while the other is dimension 2, can A be undiagonalizable? Explain.

Answer for all 3 questions required.

Expert Solution

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Colby Messinger answered 2 years ago

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