1. [5marks] Consider the dynamical system: SH]-[ ] and Lo]- 0 1 1 Or using separate equations we might write: 2 *n+1 =-4)n XO=0 3 Vn+1 = XM No =1 [a) Use the recursive equations to fill the entries in the table at the 5 right. 6 7 (b) Based on the pattern found in the table give me a formula for *. for any given n. Actually there isn't a simple single formula 8 using real numbers, but there is a simple 2-part formula, one for even n and one for odd n. Give me these. [This part is actually a 9 high school problem-just use the pattern in the table.] (c) However,using the eigenvector method, we can get a single complex formula for x. The formula you obtain will look complex, but make it clear that it always gives a real number by writing it as the real part of a complex number. As a check use your formula to calculate Xa and X9 and compare with your values in the table