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2 1 1 1 0 1 1 1 0 These questions have got me confused: 1....

2 1 1
1 0 1
1 1 0

These questions have got me confused:

1. By calculation, I know this matrix has eigenvalue -1, 0, 3 and they are distinct eigenvalues. Can I directly say that this matrix is diagonalizable without calculating the eigenspace and eigenvectors? For all situations, If we get n number of answers from (aλ+b)n , can we directly ensure that the matrix is diagonalizable?

2. My professor uses CA(x)=det(λI-A) but the textbook shows CA(x)=det(λI-A). which one is correct?

Thank you very much.

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