Write the answer in terms of the weights x o and y$.$ What is the gradient descent for each weight. Not actually solving for anything write answers in matrix form. Question $2.$ The machine below $($Example $3\mathrm{.}7)$ recognizes any string of $0$s whose length is a power of two.

a$)$ Give the configuration of the machine on input $0^{(2^3)}$ immediately after its second $q_2$ to $q_3$ transition. Hint: Note that the book gives the entire configuration sequence for the machine on input $0^{(2^2)},$ and the configuration of the machine on this input immediately after its second $q_2$ to $q_3$ transition is $q_{3}x.$

b$)$ Give the reject configuration of the machine on input $0^7.$

c$)$ Give the reject configuration of the machine on input $0^6.$