# Answer to Question #1379 in Linear Algebra for AA

Question #1379

(a) Let A be a square matrix and fA(x) (x = lambda) its characteristic polynomial. In each of the following cases (i) to (iv), write down whether

(D) A is diagonalizable over R

(N) A is not diagonalizable over R

(U) it is not possible to say one way or the other.

(i) fA(x) = (x - 3)^2(x - 5)

(ii) fA(x) = (x^2 - 1)(x^2 - 2)

(iii) fA(x) = (x^2 + 6)(x - 1)(X + 2)

(iv) fA(x) = (x^2 + 3)^2

(b) For each case that you marked (N), say whether or not the matrix can

certainly be diagonalized over C

(D) A is diagonalizable over R

(N) A is not diagonalizable over R

(U) it is not possible to say one way or the other.

(i) fA(x) = (x - 3)^2(x - 5)

(ii) fA(x) = (x^2 - 1)(x^2 - 2)

(iii) fA(x) = (x^2 + 6)(x - 1)(X + 2)

(iv) fA(x) = (x^2 + 3)^2

(b) For each case that you marked (N), say whether or not the matrix can

certainly be diagonalized over C

Expert's answer

Your question requires a lot of work and cannot be done for free. Submit it as an assignment to our control panel and we'll assist you.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment