Suppose there are three birds flying in the sky and assume the birds' speeds are v(k), v(k) and v3 (k) at moment k, respectively. Each bird will adjust its speed based on the average of the other two birds' speeds, i.e. at moment k + 1, the birds' speeds are v(k+1)= v(k) + v3(k) 2 respectively. Assume the initial speeds are (0) = 8m/s, 2 (0) = 9 m/s and v3 (0) = 13 m/s. 1. What are the speeds of the birds at moment k = 1? vi (k+ 1) = v(k) + vs(k) 1 2 v(k) + v(k) 2 and v3(k+1) = 2. Assume we lump the speeds into a vector as z(k)= [v(k), v(k), v3 (k)]TE R, then the relation between z(k+1) and a(k) can be described as r(k + 1) = Az(k) with A & RX. Find the A matrix. 3. Find a canonical diagonal matrix similar to A, and give the orthogonal transformation matrix. 4. Find the speeds of the birds when k, i.e. lim x(k).