(1.5) Investigate the complete controllability of the linear autonomous system J=-2y+u y=-x+y in the following two cases: (a) If the control u is unbounded. (b) If u(t)| ≤ 1 for all t≥ 0.

Q: m. (ii) Describe the set of production efficient output ation and illustrate the production…

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Q: (b) (c) Select the graphs above that represent a non-linear negative association between the…

A: Correct answer is (D) Graph (c)

Q: 1/2 Consider a consumer with the utility function u (x1, x2) = x₁¹ + x2. Suppose the cost of…

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Q: Consider the system i = f(x)+ g(x)u iere sin x2 f = COS x2 g =

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 5x + y + 3z, subject…

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Q: Let T(x, y, z) = x² + y² + z² and h(x, y, z) = 2x + 3y - 5z + 4. Which one of following systems of…

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Q: True or False Equilibrium (0, 0) is a center of the linear system dY/dt = | 1 3   |…

A: Given the system is dYdt=13-32Y. Given statement is "The equilibrium 0,0 is a center of the linear…

Q: 5. A firm produces two goods are substitutes and the demand and total cost functions are: P = 120 –…

A: The Hessian determinant is a square matrix of second ordered partial derivatives of a scalar…

Q: Find the minimum and maximum of f(x, y, z)= ² + y² + subject to two constraints, 2+2y+z= 2 and a- y…

A: Given: fx, y, z=x2+y2+z2Subject to constraints:x+2y+z=2x-y=6 To Do: Find maximum and minimum values.

Q: Consider a linear time invariant system i = Ar, x(0) = [0, 1, 1] = R³ with 2 -1 1 A = 1 0 0 0 -2 -

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions X₁…

A: given with

Q: In addition, if h(t) = 0, when t< 0, the system is said to be causal. 2. If the input to a…

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Q: The functions f(r) = 4t3 and g(r) = 3|1| are linearly independent on (-0, o∞) Select one: True O…

A: Given a statement

Q: Find the minimum and maximum values of the function f(x, y, z)= 3x +2y + 4z subject to the…

A: Maxima is the maximum point of the function and minima is the minimum point of the function.…

Q: EXERCISE 5. Consider the function f(x,y) = x(1- y²) in the domain {(x, y): r² + y² = 1}. (a)…

A: Given function is fx, y = x1-y2 Domain = x, y : x2+y2=1

Q: #6: Let A = 8 0 2 and b = Find the least squares solution of the linear system Ax = b. Enter the…

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Q: Find the minimum and maximum values of the function f(x, y, z) = x - y-2° subject to the constraint…

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Q: he output of a good is y + avx, where x and y are he amounts of two inputs and a > 0 is a arameter.…

A: *answer:

Q: (ii) Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Goods A and goods B are produced and sold by the company according to the following equation: P₁ =…

A: The Profit function is…

Q: Find the maximum and minimum of the function f(x,y) : 1 subject to the x² + 2y² constraint x* +2x²y²…

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Q: The system shown below contains two linear shift-invariant subsystems with unit sample responses h₁…

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Q: Consider the controller form of a single-input single-output linear system. 1 ... ... i(t) = x(t) +…

A: We will use induction to solve the part (b)

Q: Find the point where the function f(r, y) = r² + 4y² + 12 subject to the constraint z + y = 5 takes…

A: f=x2+4y2+12..............(1) the given constraint is  x+y=5 y=5-x................put it back in…

Q: Suppose we are able to model the total utility function for the consumption of two goods, good x and…

A: Given Utility Function :  U(x, z) = 3x2 + z2 - 2xz Px = Py = $1 Total Income = $1000

Q: Imagine a predator–prey interaction in which a certain number of the prey population cannot be eaten…

A: Given: Predator- prey interaction with refuge in their environment Interaction terms: -sP-wQ, vP-w,…

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

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Q: Analyze the stability of the critical point of the following system, proposing as a Lyapunov…

A: (a) To Analyze the stability of the critical point of the following system, x'=-2xyy'=x2-y3 By using…