Suppose there are three birds flying in the sky and assume the birds' speeds are v(k),...

  

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Suppose there are three birds flying in the sky and assume the birds' speeds are v₁(k), v₂(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 v₂(k+1)= v₁(k) + v3(k) 2 respectively. Assume the initial speeds are ₁ (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) = v₂(k) + vs(k) 1 2 v₁(k) + v₂(k) 2 and v3(k+1) = 2. Assume we lump the speeds into a vector as z(k)= [v₁(k), v₂(k), v3 (k)]TE R³, then the relation between z(k+1) and a(k) can be described as r(k + 1) = Az(k) with A & R³X³. 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). Suppose there are three birds flying in the sky and assume the birds' speeds are v₁(k), v₂(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 v₂(k+1)= v₁(k) + v3(k) 2 respectively. Assume the initial speeds are ₁ (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) = v₂(k) + vs(k) 1 2 v₁(k) + v₂(k) 2 and v3(k+1) = 2. Assume we lump the speeds into a vector as z(k)= [v₁(k), v₂(k), v3 (k)]TE R³, then the relation between z(k+1) and a(k) can be described as r(k + 1) = Az(k) with A & R³X³. 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).

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Given that v8ms Also we have V0 9 ms Vg0 13 ms VIK1 VK V3K 2 V k1 V3k Vk 1 we have to find the speed... View the full answer