breif answers will be fine thanks !

(1 point) 3 -2 -2 The matrix A = 2 1 0 0 2 5 has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. eigenvalue = multiplicity = dimension of the eigenspace = Is the matrix A defective? (Type "yes" or "no")(1 point) Suppose A is a square matrix and v is an eigenvector of A with associated eigenvalue 44. If x is a real number, compute A(xv) in terms of x and v A(xv) =[:] (1 point) Find the characteristic polynomial of the matrix in terms of b,c, and x (the indeterminate of the polynomial). 120:) = Note: In order to receive credit, you must find the characteristic polynomial with the highest power term with a coefficient of 1. That is, any answer of the form sz. . ., where C is a constant not equal to 1, will not be counted correct. (1 point) Suppose that a fourth order differential equation has a solution y = 5e3xx sin(x). Find the initial conditions that this solution satisfies. y(0)= y'(0)= y"(0)=l y\"'(0>=. (1 point) Solve the following differential equation: y" + 9y = 0; y = 3, y' = 3 at x = 1/3. Answer: y(x) =(1 point) Solve the initial value problem Ay" - By = 0 y(0) = a y (0) = b in terms of A, B, a, and b. You may assume A, B > 0. y(x) =\f