1. The problem statement, all variables and given/known data Find the eigenvalues and associated eigenvector of the following matrix: 2. Relevant equations 3. The attempt at a solution We have a theorem in our lectures notes that states that if a matrix is invertible the only eigenvector in its kernel will be the zero vector. In order to find out if it is invertible we get the det(A) and see if its equal to 0 or not, if it is equal to 0(you cant divide by 0) then there is no inverse, if it is not equal to 0(like in this case I got 6) then it is invertible and the only vector is the zero vector in the kernel. So technically I should stop my calculations at this point and say the zero vector is the only one. However in the solutions given to use they have an answer that is not a 0 vector. 1,2,3 are eigenvalues. How is this possible?