Write the system in matrix form x' = 3x – 4y + z + t, y' = x + 2y – z + t?, z' = 6y – 7z + t3

Q: 8. Find a fundamental matrix of the system y' = Ay if o\ A= 0 -2 0 -2 -2 1 1 and check your answer…

A: Explanation of the solution is given below....

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: Solve the given linear system by LU factorization method having U as unit diagonal. x + 3y + 8z = 4…

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Q: For back substitution with a band matrix (width w ), show that the number of multiplications to…

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Q: Illustrate how constant coefficients are used for elimination for constructingthe general solution…

A: To Describe : Homogeneous systems of equations with constant coefficients can be solved by the…

Q: Find the general solution of the given system by applying matrix method. dx x + y dt dy = -2x - y dt

A: system of differential equation dxdt=-x+ydydt=-2x+y To find general solution of the given system by…

Q: Solve the system equations 3x+y+2Z3D3 , 2x-3y-z=-3, x-2y+z=-4 using Jacobi's method

A: Given : 3x+y+2z=32x-3y-z=-3x-2y+z=-4 Now we solve these equations by Jacobi Method

Q: Consider the system X' = AX+B, where B= .If a fundamental matrix for the corresponding sint then the…

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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: i = r(a – r) ở = sin? +b, 2

A: The fixed point is the point where the time rate change of the system is zero. i.e. for an equation…

Q: How many solutions will the linear system Ax = b have if b is in the column space of A and the…

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Q: () Write the linear system in matrix form. Assume X = dx 3D —Зх + 5у — 92 dt dy 3 4x — у dt dz = 10x…

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Q: () Write the given linear system in matrix form. Assume X = y dx = -7x + 4y – 9z dt dy = 3x – y dt…

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Q: We try to fit a circle with center (C1, c2) and radius r in a least-squares sense to n given points…

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Q: Write the given linear system in matrix form. Assume X = dx = 8x – 2y dt dy 3D 7х + Зу dt X' = X +

A: I have written in the form and also verified. Here the system is homogenous so  last vector will be…

Q: dy dt 2x+y z3t²

A: We can write the given Linear system in matrix Form .

Q: 8t Given the second order ODE y"+6 sin(5t)y' 4e"y = cos(8t). - A. Convert it into a system of first…

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Q: Write the given linear system in matrix form. Assume X = y dx 3 —Зх + 5у — 92 dt dy — 2х — у dt dz…

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Q: Find a basis for the solution space of the given homogeneous linear system- X – 2x, +3x, 2x, - 3x,…

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Q: 2y, -Bxy +ry2. B. alues of a, B and y that make this system Hamiltonian. system. and are some…

A: Sol

Q: 14-Consider the Lie nard equation - (u-x²)x + x = 0. The Jacobian matrix for the linearized system…

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Q: Consider the system of linear equations in x and y.ax + by = ecx + dy = fUnder what conditions will…

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Q: Solve the system Y1 = 26y1 + 13yY2 + 13y3 Y2 = 13y1 + 26Y2 + 13y3 %3D Y3 = 13y1 + 13y2 + 26y3 NOTE:…

A: Given system of differential equation is y1'=26y1+13y2+13y3y2'=13y1+26y2+13y3y3'=13y1+13y2+26y3…

Q: Write the given linear system in matrix form. Assume X = dx — Зх + 5у — 9z dt dy — 2х — dt — у dz —…

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Q: Solve the system using either Gausslan elimina terms of the parameter t.) 3x +3y + 12z = 6 9. x + y…

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Q: Compute the matrix exponential e At for the system x' = Ax given below. x²₁ = 20x₁ − 20x₂, x′2 =…

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Q: Let Au + u = x^2 + y for x and y be in (0, 1). u(x, O) = x^2, u(x, 1) = x, u(0, y) = 0, u(1, y) = 1.…

A: We are given the following differential equation with the boundary conditions.…

Q: Write the given linear system in matrix form. Assume X = y dx = x - y + z + t – 1 dt dy 7x + у - z -…

A: Given - dxdt = x - y + z + t - 1dydt = 7x + y - z - 5t2dzdt = x + y + z + t2 - t + 7 To find - Write…

Q: Use carmer's rule to solve the system  x+2y-4z = 0 2x+5y      = 4         y- z   = 3

A: Firstly find ∆,∆x,∆y  and ∆z .If ∆,∆x,∆y,∆z≠0 then system has unique solution.and solution is…

Q: Explain all methods of elimination for constructing the general solution of a homogeneous…

A: To Explain: All methods of elimination for constructing the general solution of a homogeneous…

Q: Find the general solution of the system of DEs

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Q: y = y ý = Find a base matrix for the system and t=0 Solve with the condition

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

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Q: Write the given linear system in matrix form. Assume X = y dx -t 3D —2х + Зу +е" sin(2t) dt dy -t =…

A: Givendxdt=-2x+3y+e-tsin(2t)dydt=5x+9z+3e-tcos(2t)dzdt=y+6z-e-tAlse we can…

Q: Solve the system of linear equations 3x,-x, = 2 * +4x, = 5 using Jacobi iterative method with an…

A: Given,System of linear equations-3x1 - x2 = 2x1 + 4x2 = 5x° = (0,0) is the initial approximation.We…

Q: Solve the system 2x + 8y - z = 11 5x – y + z = 10 -x +y + 4z = 3 by using Jacobi Method with x° = y°…

A: We have to find the solution of the system by using Jacobi Method.

Q: =-2y-y +sin x sis y =4y +2y, + cos x

A: First find fundamental solution of the matrix.

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

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Q: Show that (12z + 1, 10z - 1, z) satisfies the system for z = 0.

A: Given system Now we have to verify (12z+1, 10z-1, z) is a solution set to the system or not.…

Q: What relation should the coefficients have so that the system has infinitely many solutions?

A: Let ax+by=c and mx+ny=p are two equations.

Q: Use Cramer's rule to solve for x. The system of equations given by x+ 2y + 2z = 1 1 -x+3y = 2 - - x+…

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Q: Write the given linear system in matrix form. Assume X = y dx -t — - 2х + Зу + e' sin(2t) dt dy -t =…

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

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Q: A system of particles are located on the x-axis with masses (in kg) 7, 12, 2, 10, and 3 whose…

A: We have, a system of particles are located on the x-axis with masses (in kg) 7, 12, 2, 10, and 3…

Q: Solve the system for (x, y, z) in terms of the nonzero constants a, b, and c.

A: ax-by+2cz=-4   →1ax+3by-cz=1       →22ax+by+3cz=2      →3 Now subtracting equation (1) from equation…

Q: Find a system of two equations in three variables, X,, X2, and x3, that has the solution set given…

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Q: Please find the problem statement attached.

A: Consider the given matrix function,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.