9. discuss the behavior of the dynamical system xk+1= Axk where (a) A = |"1.2 0.3 1.5 -0.31 0.4] a) A = [2 (b) A = -0.3 1.1]

Q: Exercise 3.6.1. Find the general solution for the system -3 2 x = ( ²2 _³ ) x + cos(2¹) ( _ )+(²).…

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Q: 4. (a) Indicate the kind of linearity (variables or parameters) the following equations exhibit: 1 1…

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Q: 36.) Solve the following System of equations BOTH graphically and algebraically. x² + y? = 5 y 2x

A: 36. These are circle and straight line passing through origin.  By graphically it shows that they…

Q: 9. discuss the behavior of the dynamical system xk+1= AXk where 0.3 (a) A = 1.2 21 (b) A = L"0.3 1.1

A: For judging the behaviour of the dynamical system, we have to calculate the characteristic  roots of…

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Q: and z. Consider a system of three linear equations with three variables x, y. [12 0 4 2 12 such that…

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Q: 4. 201 A = 2 1 -1 31-1 0-1 1 A¹ = 15 -4 12-2 Use the information above to solve the system of…

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Q: 4) Consider the system with the following input-output relation with x(t) and y(t) being input and…

A: This is not memory less because it depends on the past. This is not time invariant because…

Q: Use Gaussian elimination to solve the system of equations x1 + 5x2 -2x1 - 7x2 a) b) = 7 = -5 x1 -…

A: We have to solve system of equations using gauss elimination method.

Q: question B

A: Part(A)   x+2y−z=12x=12−2y+zThe system of linear equations has 3 variables and one equation. Thus,…

Q: 4. Find the first four successive approximations u(¹)(t,a), u(²)(t,a), u³(t, a), and u(4) (t, a) for…

A: Ans- To find the successive approximations, we first need to write the system in normal…

Q: Given that p(x) ax³ + bx² + cx + d is a polynomial of degree 3 such that p(-2) = 3, %3D p(3) = 11,…

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Q: ge the observability of the following systems. (2) = 0 0 0 1 -4 0 0 0 0 0 -3 0 0 0 10 72x 21 X

A: The observability of a linear time-invariant system is determined by the observability matrix. For a…

Q: 1.4 Consider the system х+2у + 3z %3а 2х + 5y + (а + 5)z %3D —2 + 2а -y + (a² – a)z = a² – a Find…

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Q: 1 0 2 Let A =| 2 11 -1 3 3 2 (b) Use part (a) to solve the linear system A y -2

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Q: Consider the following nonhomogeneous linear system: x = y + et = -2x + 3y + 2 y = 1.Which of the…

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Q: udge the observability of the following systems. -1 (x = [²₁ = 3] x + [₁¹] ₂ -3 (x= [¹₁8]x 1 X

A: Observability is a property of a system that determines how well its internal states can be inferred…

Q: EXAMPLE 6.41 Find queue length of the system if λ = 12 per hour, μ = 4 per hour, Po= 0.0313, and c =…

A: Find queue length of the system if  λ= 12 per hour. μ = 4 per hour. P0= 0.0313 and  c = 4

Q: 10. Consider the following transfer-function system: Y(s) U (s) = S+6 s² + 5s +6

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Q: 2. Determine (a) (b) (c) 1 0 0 if a solution to the linear system exists. If so, is it unique? 3 0 0…

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Q: 16. A playing field measures 120 m by 240 m. Karen wants to mow two-thirds of the field by mowing…

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Q: 4. Check the input-state linearizability of the system: x, + x,+x} x, d x2 = 2| x, + sin(x,-x,)+0 u.…

A: To verify whether the given state space system is linearizable we have to find the Jacobian of the…

Q: 3.24 Find a Liapunov function for the system Y, y' - 4.x – cy - where c > 0.

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Q: Given the linear system Ax = b 3 -1 [x1 X2 b2 ,and A LU decomposition is A = b3 1 0001[1 3 -1 21 -1…

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

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Q: 1. Consider the following nonlinear system: ài = fi(r1, r2, r3) + 91 (a1)u à2 = f2(a1, #2, 23) %3!…

A: Given,x1.=f1(x1,x2,x3)+g1(x1)…

Q: 07) (:) - () 0.8 0.3 0.6 For the system then the value of u is 0.2 0.7 0.4

A: Here we use matrix inverse method to find the value of u.

Q: 0 1 ,then the matrix is 1 0 (a)positive definite (b) negative definite (c) -Tx] [j1. Q29. If A =

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A: Given: a+1xy'-d+1y=cosyx For, a=1, d=6. We have, 2xy'-7y=cosyx …1

Q: x1 + 2x2 – 3x3 = -2 Find the value of k for which the system of equations 3.x1 – x2 – 2x3 = 1 2.x1 +…

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Q: 1.2.12 (a) Explain why every linear system over R has either zero solutions, one unique solution, or…

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Q: 5. Let -4 | 2 -5 3 mpute A¹ and use it to solve the system Ax = b. A = -3 and b =

A: We have systemwhereWe have to solve using inverse method.

Q: 1. Find y by Cramer's rule for the following linear system. x+Oy+2z 6 - 3r+4y+6z= 30 -r-2y+3z S

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Q: A single-input, single output system has the state variable representation a. b. O d. where A = =…

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