I have to be able to figure out eigenvalues and eigenvectors for 2x2 and 3x3 matrices for my physics course, but I have never taken linear algebra so I obviously have no idea what they even are. I need someone to basically teach me how to solve these problems because I have no knowledge of this material and cannot find any useful source to help me. First I have to find the eigenvalues and vectors for [a 0 1] [0 b 0] [0 0 c] where a =/= b =/= c. I looked around online and could only find that the answers for the eigenvalues are a, b, and c but I have no idea how that answer is derived. And I have no idea how to solve for eigenvectors except so any help would be great. Next I have to do the same thing for [a a 0] [2a 0 0] [0 a a] where a =/= 0. Again I know that the solution for the values is -a, a, and 2a but no clue on how to actually do the problem. I know nothing of this material except how to figure out the determinant of a matrix. So detailed steps on how to solve for eigenvalues and eigenvectors would be greatly appreciated.