Let Show that: If the homogenous system AX = 0 has only the trivial solution, then ad – bc # 0.

Q: Solve the linear system Ax = b by using Cramer’s rule,givenCarefully explain all steps in your…

A: Given: A=342122301b=1−14

Q: Find the value of for which the system X-y = -2 is inconsistent. a X+ay = a

A: The solution for the above question is as shown below.

Q: consider an arbitrary linear system with input x[n] and output y[n]. show that x[n]= 0 for all n…

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Q: (a) Compute eAt for -1 A Solve the following linear nonhomogeneous system: et x1 = x1 – x2 + t2 +1 x…

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Q: I2 + 13 I2 + I3 2x4 = 0 = 0 I3 + T4 = 0

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Q: Represent the given system by matric representation. 2x+4y =5 -x +3y =-2

A: Given a system of equation.  2x+4y =5- x +3y =-2 We have to represent the given system by matric…

Q: Determine whether the nonhomogeneous system Ax = b is consistent. If it is, write the solution in…

A:

Q: Exercise 1.2.8 In each of the following, find (if possi- ble) conditions on a and b such that the…

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Q: Determine whether or not the following system is asymptoti- cally stable: 1 X'(t) = AX(t), A = 300…

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Q: In the system of constant. For w ехас exactly one dist

A: Concept:ax2 + bx + c = 0can have only one solution when,when the discriminant is zero.b2-4ac = 0b2 =…

Q: 4. Consider a nonhomogeneous system (I): Ar = b and the associated homogeneous system (II):Ar = 0.…

A: Given A non-homogeneous system is                                                        Ax=b…

Q: A discrete-ti" system is described by the following parameters [0 0 A = |0 1 0 B = D = 1 (a) Check…

A: Answer for sub question a: The given time discrete LTI system is not internally stable. A time…

Q: 12.Consider the linear homogeneous system x'=p11(t)x+p12(t)y,y'=p21(t)x+p22(t)y Show that if x =…

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Q: Let -3 M and A 0. 2 Solve the second-order system Mx" = Ax, where r(t)

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Q: Consider the two-dimensional system: ở = y+x (x² + y*) * (2² + y² – 1)² ; ÿ = -x+y (x² + y³) * (x²+…

A: Given: The two dimensional system, x˙=y+xx2+y212x2+y2-12 y˙=-x+yx2+y212x2+y2-12 The Lyapunov…

Q: Verify that the following linear system does not have an innite number of solutions for all…

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Q: Consider a system with the following state-space representation X(0) = [₁]x+but) x(t) What values of…

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Q: Suppose that the given system has one solution. ajx + b¡y = c, azx + bɔy = c2 and and where D = Ds…

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Q: Determine whether the nonhomogeneous system Ax = b is consistent. If it is, write the solution in…

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Q: linear system does not have an infite number of solutions for all constants b. x1 + x2 - x3 = 1 2x1…

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Q: Determine whether the nonhomogeneous system Ax = b is consistent. If it is, write the solution in…

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Q: Consider the following nonhomogeneous linear system, 4 -1 1 0 2 I' = 0 0 I+ g(t) -1 Determine a…

A: Note:- As per our guidelines, We can  answer the first question since the exact one wasn’t…

Q: 1.2.10 Show that if ad – bc # 0, then the linear system ах + by 3D е cx + dy = f has a unique…

A: A linear system of equations is a collection or set of more than two equations of first degree…

Q: Find all real number 1 such that the homogenous system such that (AI – A)X = 0 has a nontrivial…

A: A=-2000-23045 Consider, λI-AX=0 ⇒λ+2000λ+2-30-4λ-5x1x2x3=0

Q: Show that the 3D system x' = Ax is conjugate to the system x' = -x where a < 0 and A is given by (a…

A: To prove that the 3D system x'=Ax is conjugate to the system x'=-x where A is given by  A=α100α100α,…

Q: Exercise 1.2.18 Determine if the system is consistent. If so, is the solution unique? x+2y+z-w=2…

A: The objective is to determine if the given system is consistent and if it is whether the solution is…

Q: 2. Determine if the systems with the following input-output relationships are linear and/or time…

A: Answer for sub question d: For a system yt=fxt, if y1t is the response to x1t and y2t is the…

Q: 3.40 Compute the response of the system ytn) = 0.7y(n - 1)-0.12rin - 2) + x(n-1)+x(n -2) to the…

A: Determine the z-transform of the function. Now determine the stability function which is Hz and then…

Q: 1. Determine whether or not the following systems have a periodic solution. (b) %3D y +x – x² 1+ y…

A: Find the Fx and Gx after that Fx+Gx, this value is  same sign then it has a no periodic solution.…

Q: (a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that…

A: We have to show that solution of given system can be written as x=p+z.

Q: a system is constructed from two functions as , proof that such system is linear using a…

A: In the given question, the concept of  Superposition Theory is applied. Superposition Theory…

Q: Show that the Wronskians of two fundamental sets of solutions of the system x' = A(t)x can differ at…

A: Consider the given equation. x'=Atx The abels formula is defined as. Wt=ce∫a11t+⋯+anntdt Let's…

Q: 1- Let A- then AT .. 2- Let C =-4 5 and D -21 = [8 find C.D. 3 -4 %3D 4 3- Use Gramer's rule to…

A: To answer the given question based on matrices.

Q: 9. Find a basis for the space of solutions for the homogeneous linear system AX =0. Hint: Remember n…

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Q: Find a general solution of the given ODE (a) by first converting it to a system, (b), as given. у" +…

A: Thanks for the question :) And your upvote will be really appreciable ;)

Q: Investigate input-to-state stability for the following systems x, =-x, +xx2 (x2 =-x}-x, +u

A: From the given system it is clear that it is a non-linear system( containing x12 and x13 terms). As…

Q: Determine whether the nonhomogeneous system Ax = b is consistent. If it is, write the solution in…

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Q: 'ind conditions that the b's must satisfy for the system to be consis- ent. 6x – 4y = b1 ||

A: Find the order pair (x,y) that can make                            6x-4y=b1and        3x-2y=b2 both…

Q: Solve the following linear system by Cramer's Rule: -2X+ Y+ Z= 4 -4X+ 2Y– Z = 8 -6X – 3Y+ Z = 0

A: By the Cramer's rule X=DXD,Y=DYD and Z=DZD .To solve the given system of equation using Cramer's…

Q: Let A = - 1 Determine whether the Jacobi method applying for solving the linear system

A: The given matrix is 1-111

Q: Show that the 3D system x' = Ax is conjugate to the system x' = -x where a < 0 and A is given by 1 A…

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Q: 3) Show that there are no nonconstant periodic solutions to the following system. x' = x + y + x³ –…

A: Taking β(x,y)=1, and comparing the given system with theorem 7.4, we get x'=x+y+x3-y2=f(x,y) and…

Q: Show that the system 1 3 dt has a fundamental solution set {x(t), x2'(t)} , where X x(t) = (;)e' and…

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Q: Prove that a linear system Ax = b is consistent if and only if the rank of (A | b) equals the rank…

A: Assume, Ax = b is consistent. Then in the column space of A lies B. Therefore, the dimension of the…

Q: Prove or give a counterexample to the following statement: If the coefficient ma trix of a system of…

A: Given: If the coefficient matrix of a system of m linear equations in n unknowns has rank m, To…

Q: Consider a system with the following state-space representation X(t) = [₁]x(t) + B₂Ju What values of…

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Q: 1) If the responses of a linear system are yl, y2 for the inputs of xl,x2, respectively, give the…

A: Use the property of superposition to solve the following problem. Additivity and superposition are…

Q: Evaluate the following linear system using Cramer's Rule: a. x-3y +3z=-4 2x+3y-z=15 4x-3y-z=19

A: The given system of linear equations…

Q: Use Cramer's rule to solve the following linear system in x and y: + 5y + dy 3x P, Cx || in which c,…

A: Solution of given system by using Cramer's rule as follows

Q: pls explain to me step by step and dont skip any step. i will rate your answer immediately. thanks a…

A: To analyze the given non-linear system at its critical point(s)