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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_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_forwardHow much longer should you expect Gaussian elimination to work on a system of 1000 equations versus a system of 500 equations?arrow_forward
- Find the general solution of the given system.using matrices dx/dt = -5/2x + 4y dy/dt = 3/4x-3yarrow_forwardFind the general solution of the given system. dx/dt = 4x-y dy/dt = 16x-4yarrow_forwardfirst write the given system of differential equations in matrix form, and then determine all solutions. Q. x′ 1 =3x1−4x2−x3, x′ 2 =− x2−x3, x′ 3 =− 4x2+2x3.arrow_forward
- Find the general solution of the given system. dx/dt=3x-y dy/dt=9x-3yarrow_forwardConsider 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_forward
- 1) For the following system of homogenous linear equations:x-y+8z= 0 -x -3z= 0 2x+y+z= 0 Use elementary row operations to solve the above system. Identify the free variable(s) if any.arrow_forwardFind the general solution of the system of equations {dxdt= −7x − 8y {dy/dt= 10x + 11y.Use your solution to solve the initial values problem{x(0) = 2{y(0) = 2arrow_forwardWrite down the augmented matrix [A b] with an extra column:X + 2y + 2z = 14x+8y+9z = 33y + 2z = 1Apply E21 and then P32 to reach a triangular system. Solve by back substitution. What combined matrix P32 E21 will do both steps at once?arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning