(2 points) Consider the sequence defined recursively by a₁ = 1, a2 = 2, an+1=-5a-1-6an. We can use matrix diagonalization to find an explicit formula for an a. Find a matrix that satisfies an an-1 == M an+1] an M b. Find the appropriate exponent k such that an = Mk ዐ1 a2 an k = || c. Find a diagonal matrix D and an invertible matrix P such that M = PDP-1 D= d. Find P-1 P-1= e. Find M5 PD5P-1 M5 = f. Use parts b. and e. to find a6. a6 P 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.