The Tribonacci equation is similar to the Fibonacci equation, but it is defined by the previous three terms instead of the previous two, i.e. T (n) is defined by

T(0)=0,T(1)=1,T(2)=1,T(n+1)=T(n)+T(n?1)+T(n?2), for n?2.

Use Matlab

(a) let R(n) = T(n?1) and S(n) = T(n?2), we can come up with a linear recurrence relation for the Tribonacci equations similar to the ones we came up with for the Fibonacci equations. Write that system of equations

(b) Translate the linear system to a matrix equation.

(c) Use your matrix recursion to quickly find the 200th Tribonacci number. Do not use loops, recursion, or any other technique.