Question 1: Let A be a non-square matrix, say m x n for m is different from n, Then C = and are both matrices, but of different sizes.
Show that C and D both have the same non-zero eigenvalues. [Hint: write down the equation that must be satisfied by a vector v to be an eigenvalue , and try to adjust that equation so as to find an eigenvector of D with the same eigenvalue. you will need to explain why your proposed eigenvector is not O.]
Question 2: Is there a 3 x 3 symmetric matrix with eigenvalues and corresponding eigenvectors Either find the matrix or explain why it can not exist.