Explain the concept of Nonhomogeneous Linear Systems ?

Q: Calculate A1, A2, A3 for the dynamical system An+1 = 4An + 3, where A, = 6.

A: Given By substituting n=0, we get By substituting n=1, we get By substituting n=2, we get

Q: Give attention to a nonhomogeneous linear system of the form?

A: The non-homogeneous linear systems of the form are-

Q: Explain the Stability of Linear Systems theorem ?

A: Consider the definition for the stability of the Linear systems theorem for the y’(t) = Ay(t).

Q: What do you mean by trajectory of the system ?

A:

Q: A linear system in echelon form is necessarily a consistent linear system. True

A:

Q: Give an example of a non-trivial (i.e. not the zero matrix) homogeneous system of three equations in…

A: linear equations has infinitely many solutions

Q: use Cramer's Rule to solve the given linear system x + y - z = 1   x+y+z=2   x-y = 3

A:

Q: Explain the four possibilities for a nondegenerate trajectory of the autonomous system ?

A: Let the nondegenerate trajectory of the autonomous system is given as:

Q: Explain the importance of fixed point in discrete dynamical Systems with the help of two practical…

A: For finding fixed point we make dx/dt=0 and then  we  solved it. After that for stability we…

Q: Explain the properties of a nonhomogeneous system?

A:

Q: What does it imply when systems are interconnected, and to what degree are they interrelated?

A: There are many ways to define the system. A system is group of interacting elements.

Q: Define concept of Almost Linear Systems ?

A: Given Concept of Almost Linear System Definition       A non linear system is almost linear at an…

Q: Define a Gallery of Solution Curves of Linear Systems?

A: Consider the homogeneous system of equation:   x’= Ax   Where A is n*n matrix   Suppose that A is an…

Q: The metal plate has constant temperature shown on its boundaries. Find equilibrium temperature at…

A:

Q: 3 x = x³ = x

A: To find equilibrium point , we equating the differential equation equal to zero.  let the…

Q: Is it possible for a nonhomogeneous system of seven equations in six unknowns to have a unique…

A:

Q: Consider the system i = -y – x, y = x .

A: The system of non-linear differential equations are given as x.=-y-x3y.=x two show the linearization…

Q: Use variation of parameters to solve the given nonhomogeneous system. X = ( 9 8)x + ( )

A:

Q: The accompanying figure shows a network of one-way streets with traffic flowing in the directions…

A: Flow is one way so all the values of x must be non negative.

Q: Mr. Edwards has a total of 28 kids in his class or six more boys than there are girls ready system…

A: Total kids=28 Ler ‘B’ =No of boys in class Let G =No of girls in class So B+G =27 ------equation 1

Q: What operations can be performed on a linear system to arrive at an equivalent system?

A: To perform: - "operations on a linear system to arrive at an equivalent system"

Q: Mark the following statement true or false: Every homogeneous system of linear equations has a…

A: Every homogeneous system if linear equation has a solution.

Q: What can you say about the solutions to the consistent nonhomogeneous linear system Ax = b if the…

A: The rank of A of a consistent nonhomogeneous linear system Ax = b is less than the number of…

Q: (a) Determine all critical points of the given system of equations.

A: We have to find the all critical points of the given system. For critical points dx/dt =0 dy/dt =0

Q: Now consider the case when the parameter varies slowly in time , that is consider the system…

A: The two equation in dynamical system which varies with time is…

Q: If the junction point is the origin of a nonlinear system, then the Libanov function can be used to…

A: We have to find whether statement is true or false

Q: Imagine that a system is the linearization of two systems around (0,0), which is an equilibrium…

A: The complete solutions are given below

Q: Explain Principle of Time Reversal in Linear Systems?

A: To Describe: Time Reversal in Linear System

Q: Find the augmented matrice of the linear system . x - y = 0 2x + y = 3

A: Given: x−y=02x+y=3

Q: Define a critical point of the system?

A: According to  the question, we have to define the term critical point of the system.  A critical…

Q: Consider a physical system whose

A: Given, a physical system whose three-dimensional state space is spanned by the orthonormal basis…

Q: The accompanying figure shows a network of one-way streets with traffic flowing in the directions…

A:

Q: Consider the system below. Let a = 0. x1 = -x1x3 + ax1 x2 = -x2xỉ + ax2 A) Examine the stability of…

A: To Determine :-  The stability of the origin with the linearization method. x1˙ = - x1 x22 + a x1x2˙…

Q: Find the solution for for nonlinear equation system below: F1 (x, X:) = x, + x;'e$l – 2 F2 (x1, X2)…

A:

Q: Explain “dynamical system”?

A: We have to explain “dynamical system”?

Q: 2 3 4 What is the equilibrium point of this system?

A: Equilibrium point of the system is (0, -1)

Q: Consider the nonhomogeneous system 2х, — 6х, + 3х, —-4 -X + x; + x, = 5 2.x; +6x, – 5.x, = 8

A:

Q: 9) What is the value of unstable equilibrium point of the system?

A: 9. x'=x2-4 Putting x'=0, we get  x2-4=0x-2x+2=0x=2, -2 Let fx=x2-4 Differentiating wrt x, we get…

Q: Find the first two iterations of the Gauss-Seidel methodforthefollowing linear system using x(0) =…

A:

Q: Find a homogeneous system whose solution set W is spanned by {u1, u2, u3}={(1, -2, 0, 3), (1, -1,…

A: See the attachment

Q: Determine the stability of the equilibrium points of the following systems (a) x': = ax + y – x³, y'…

A: Solution a: Given system is x'=αx+y-x5y'=-x-y5 Where α is the real number. Let f(x,y)=αx+y-x5…

Q: consider the nonhomogeneous linear system { dr * = a1 (t)x + b1(t)y + fi(t). * = a2(t)x + b2(t)y +…

A:

Q: If a solution to a linear system has a free parameter, then the system is consistent. True False

A: We have to find If a solution to a linear system has a free parameter, then the system is consistent…

Q: Explain the Nonhomogeneous Linear Equations ?

A: The system of the equation can be written as Ax=b or…

Q: Is every homogeneous linear system always consistent? Explain.

A: To, Explain if every homogeneous linear system is always consistent.

Q: Find the general solution using linear coeffecients

A:

Q: Find the final value of the system corresponding to

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.