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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_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
- 1. for the case of repeated real roots what would the general solution be?2. if i was to let y1(t) = theta(t) as well as y2(t) = theta'(t)=y1'(t) how could i show that the initial equation could be written as a system of 1st order odes that involved y1 and y2. the system will then need to be presented as a the matrix equation y' = Myarrow_forwardFind the general solution of the given system.using matrices dx/dt = -5/2x + 4y dy/dt = 3/4x-3yarrow_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_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_forwardFind the general solution of the given system. dx/dt = 4x-y dy/dt = 16x-4yarrow_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_forward
- Apply the Gauss-Seidel method to the systemarrow_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_forwardfind the general solution of the system X' = AX for the given matrix A.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning