Thread: Matrices

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

i)


ii)

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

Hello,

Originally Posted by matty888

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

i)


ii)

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

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

Originally Posted by matty888

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

i)


ii)

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

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