Solve 3 and 4

3. Let A 3 0 3 1 1 0 2 -2 0 Find all eigenvalues of A, their algebraic and geometric multiplicities. 2 4. (a) Let A be an nxn matrix such that the sum of its entries in every row is equal to r. Show that r is an eigenvalue of A. (b) Let A be an n xn matrix of the form A = al + b), where a, b E R, and I is the identity matrix while J is the 'all one' matrix (all entries are one). Find the characteristic polynomial and all eigenvalues and eigenspaces of A. = '2