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Differential Equations and Linear Algebra (4th Edition)
- Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?arrow_forwardHow much longer should you expect Gaussian elimination to work on a system of 1000 equations versus a system of 500 equations?arrow_forwardFind the general solution of the given system.using matrices dx/dt = -5/2x + 4y dy/dt = 3/4x-3yarrow_forward
- You are given the following inhomogeneous system of first-order differentialequations for x(t) and y(t) in matrix form: x ̇ = 2x + y + 3 et ,y ̇ = 4x − y Write down the general solution of the original inhomogeneous systemarrow_forward1. If y = (x + 1/x) (2x-3, then dy/dx will be ? 2. If matrix A is (2 5) (3 4) and f (x) = x2 +4 , what is the answer to f (A)?arrow_forwardI am confused with how to find the general solution of the matrix for problem 14. In this problem the general solution matrix is [-1/2 1 0],but I don't understand why that would be the general solution.arrow_forward
- Consider the following. x1' = 3x1 − 2x2, x1(0) = 3 x2' = 2x1 − 2x2, x2(0) = 1 2 (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for x1.' (b) Find x1 and x2 that also satisfy the initial conditions.arrow_forwardIt is known that the solution of the linear system, of order 3, Ax=b, is given by column x =[1 1 1] where column b=[1 1 1]arrow_forwardI am struggling to find the solution for the system x(t) and y(t), given the information highlighted in green. Can you please explain the steps to better understand?arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning