The question is, for which x is the equation $\displaystyle A_x= lambda_x $ valid? And then I am a given a square matrix of say (9 5)(first row) (6 7) (second row.)Then you are given a lambda value of say 4 which apparently is the eigenvalue and $\displaystyle x_1 and x_2$. I don't understand the question properly. I can calculate for the eigenvectors since I have the eigenvalue by subtracting them from the diagonal matrix so I will have 9-4 and 7-4 and so on and then I can find the value of x to get the eigenvector. But I don't understand the question properly. I can't multiply the vector by the matrix since it is not a square matrix so, how do you go about it? Thanks all in advance.