Matrices

Which of the matrices below are diagonalizable and which are not?Explain your answer.

i) http://www.cramster.com/Answer-Board...9200005796.gif


ii) http://www.cramster.com/Answer-Board...6326250199.gif

HINT: In both cases the only eigenvalues are λ=-1 and λ=2.

Hello,

Quote:

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Originally Posted by matty888

Which of the matrices below are diagonalizable and which are not?Explain your answer.

i) http://www.cramster.com/Answer-Board...9200005796.gif


ii) http://www.cramster.com/Answer-Board...6326250199.gif

HINT: In both cases the only eigenvalues are λ=-1 and λ=2.

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Find the eigenspaces associated to each eigenvalue.
If the sum of their dimension is 3, then it's diagonalisable.

Quote:

---

Originally Posted by matty888

Which of the matrices below are diagonalizable and which are not?Explain your answer.

i) http://www.cramster.com/Answer-Board...9200005796.gif


ii) http://www.cramster.com/Answer-Board...6326250199.gif

HINT: In both cases the only eigenvalues are λ=-1 and λ=2.

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An n x n matrix A is diagonalizable if and only if it has n linearly independent eigenvectors .....