Formulas you can use: f (t) |F(s) = [{f (t) } C pat 1 s-a in n! sin(bt) b $21 62 cos(bt) 8 $2+ 62 e cs uc(t ) S 8(t - c) e sc ect f(t) F(s - c) uc(t) f (t - c) e-cs F(s) f' SF(s) - f(0) f" $2 F(s) - sf (0) - f'(0) 1. Find the eigenvalues, the eigenvectors and if necessary, the generalized eigenvectors of the matrix A and explain why or why not it is diagonalizable: A = O given that one of the eigenvalues is 2. 2. The following is given: The matrix -5 10 1 3 4 A = and its reduced echelon form rref(A) = 0 1 0 0 0 O 0 You don't need to derive the reduced echelon form, you can take this as a fact. Find a basis for the column and null spaces of A as well as the dimension of the null space of A and the rank of A