Problem 6. Note that in this problem the matrix is not diagonalizable and has only two different eigenvalues. It is a multipart problem in which we consider the following 3 x 3-matrix ON A = -12 3 Part A. Find the two eignalues 1 and 12 and fill out the following table FINAL. MAT 315: LINEAR ALGEBRA. Eigenvalues AlgebraicMultiplicity Eigenvectors GeometricMultiplicity alg.mult(>1) = UN = geo.mult(>1) 12 = alg.mult(>2) = VAZ = geo.mult(12) Part B. Use the table above to determine the Jordan normal form J of the matrix A. Part C. One of the eigenvalues above has a different algebraic multiplicity then geometric multiplicity. This means we need to find a generalized eigenvector q. To this aim, use the matrix equation AQ = QJ to find this vector q. Part D. (Extra credit) Calculate est and uses this to calculate eAt = QeltQ-1 by using your answer in Part C. Part E. (Extra credit) Consider the non-homogouns system of differential equa- tions av = Av + b(t) where b(t) = (1, t, 0). Calculate the particular soloution Up = edtu(t) by first computing u(t) = JetAb(t)dt + C where C = (c1, C2, (3). Part F. (Extra credit) Use the initial condition v(0) = (1, 2, -1) to solve the initial value problem in Part E and write down the resulting particular solution Up