# Answer to Question #13064 in Abstract Algebra 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 0 -2

then it is its Jordan form, and it cannot be diagonalized.

it be 5. Then

if matrix of transformation has form

5 1 0

0 5

0

0 0 -2

then it is its Jordan form, and it cannot be diagonalized.

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