Problem 5. Let A be a 22 matrix with eigenvalue -1 and associated eigenvectors 1 -(0) and (1) The characteristic polynomial of A is given by p(A): (2) The algebraic multiplicity of = -1 is (3) The geometric multiplicity of = -1 is (1) det (A) (5) Tr(4) (6) Is it possible to find the matrix A? If so, then A = Problem 6. If 2 is an eigenvalue of the matrix J = 0 X 1 y 2 10 with associated eigenvec- 0 Y x -0- tor and y = then x = Problem 7. Suppose that the characteristic polynomial of a matrix A is given by p(X) A (A-1)(X+1). (1) The size of the matrix A is (2) The eigenvalues of A are (3) The determinant of A equals (4) The trace of A equals (5) The eigenvalues of 3A are (6) The eigenvalues of A are =