Consider the matrix A=
1 0 1
1 1 0
0 0 -1
a) find the characteristic polynomial of A
b) list the eigenvalues of A and their multiplicities
c) for the eigenvalues found in part B, describe the eigenvectors
d) is A diagonalizable?
a) We must find det(A-lambdaI) = so the characteristic polynomial is (1-lambda)(1-lambda)(-1-lambda) = (1-lambda)^2(-1-lambda)
b) The eigenvalues are 1,1,-1. 1 has an algebraic multiplicity of two and -1 has an algebraic multiplicity of one. What about the geometric multiplicity?
c) I'm not sure
d) No, it is not diagonalizable since the eigenvalues are not distinct (there is a duplicate)
Can someone please let me know where I went right and wrong and lead me in the right direction?