20) A discrete-time matrix model in three dimensions has the form Xn+1 ] [Xn] Yn+1 = MYn Zn+1 The eigenvectors of the matrix M are as follows: U1 = -4 with the eigenvalue My = 0.5 U2 = -6 with the eigenvalue 12 = 1.2 U3 = -3 with the eigenvalue 13 = 0.9 The vectors u1, u2, and us form a basis of Is, which you can use to define a new coordinate system, which we will call Q, R, S-coordinates. This leads to the usual diagram for diagonalizing a matrix: M Xn+1 Yn Yn+1 Zn+1 T T T-1 Qn D Qn+1 Rn Rn+1 Sn+1 20 a) Write down the matrix T from the above diagram.7-0 '0) Write down the matrix D from the above diagram. Explain briefly what it tells you about this discrete-time model. 2C J Write down an equation that would allow you to compute M from the information given here. (You do not need to actually compute it!) X100 2 0 ch Write down a mathematical expression that would allow you to compute 1'10\"] Z100 using diagonalization of M. (You do not need to actually compute it!)