5. (1 point) Consider the sequence defined recursively by a₁ = -1, a2 = 2, an+1 = -5an-1-6an. We can use matrix di- agonalization to find an explicit formula for an. a. Find a matrix that satisfies [ a ] = M [ an−1 ] an+1 an M -[= =] b. Find the appropriate exponent k such that an αι an+1 k = a2 c. Find a diagonal matrix D and an invertible matrix P such that M = PDP-1 D = d. Find P-1. '=], P = [= =]· P-1 e. Find M5 PD³P-1. M5 = =[= =] f. Use parts b. and e. to find a6. a6= g. You can find an explicit formula for a using part b. and a formula for Mk = PDP-¹. Try to develop this formula. Use your formula to verify the answer for part f.