Write ⃗x[1] in terms of ⃗x[0] and ⃗u[0]. Then, write ⃗x[2] in terms of ⃗x[0], ⃗u[0], and ⃗u[1]. Finally, write ⃗x[3] in terms of ⃗x[0], ⃗u[0], ⃗u[1], and ⃗u[2].
a) ⃗x[1] = A⃗x[0] + B⃗u[0]
b) ⃗x[2] = A⃗(A⃗x[0] + B⃗u[0]) + B⃗u[1]
c) ⃗x[3] = A⃗(A⃗(A⃗x[0] + B⃗u[0]) + B⃗u[1]) + B⃗u[2]
d) None of the above