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Answer on Abstract Algebra Question for jess

Question #13064
Define transformation T: R^3 -> R^3 by T(x)=Ax where A (3x3) matrix and has eigenvalues 5 and -2. Is A similar to a diagonal matrix? explain
Expert's answer
If it has 2 eigenvalues then one of them has algebraic multiplicity equal 2. Let
it be 5. Then
if matrix of transformation has form
5 1 0
0 5
0 0 -2
then it is its Jordan form, and it cannot be diagonalized.

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