
(1 point) For the linear system c(t1 61 X' = AX, with X(t) = A = and X(0) = g(t) (6 -6 - 4 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. L X1 = , X1= * , and 12 = - ,X - = (b) Write the solution of the initial-value problem in terms of X(t), y(t) x(t) = g(t) =
1. a) Solve the following linear ODE. dy * dx + 2y = 4x2, x > 0 b) Solve the following ODE using the substitution, u = dy (x - y) dx = y c) Solve the Bernoulli's ODE dy 1 + -y = dx = xy2 ; x > 0
For each of the following linear maps A, given by an n × n-matrix, solve the system of linear
differential equations given by x˙(t) = Ax(t), assuming that the initial condition at some time t0 is given
by x(t0) = x0:(i) A = [2 −5 0 3 ](ii) A = [−1 −2 1 −3 ] ; iii) A = [ 4 −1 4 0 ](iv) A = [5 0 −6 0 2 0 ODE Solving.PNG 3 0 −4 ]
2 2 0 0 3" (12%) Solve the linear system x"(t) AX(t) with A 0 0 4 4 a) (406) Write down the characteristic equation of the coefficient matrix λ and solve its eigenvalues, . b) (8%) Find the four independent solutions of the system.
Exercise-15: Linear system of equations-Eigenvalues 215 In Exercises through 9, solve the system X' = AX. 2. A= 4 4 - 8
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2) using existence and uniqueness theorem and (3) calculating et in two ways.
Tutorial 6-Linear Systems EXERCISE .26. Solve the system x 3x1 +3x2, 32 2x1 + 4x2 subject to x1 (0) -, 2()5 by (1) diagonalisation of A (express the system as i - Ax), (2)...
Write the system of linear equations in the form Ax = b and solve this matrix equation for x. x1 – 2x2 + 3x3 = 24 -X1 + 3x2 - x3 = -11 2x1 – 5x2 + 5x3 = 42 X1 x2 = X3 ] 24 -11 42 [ x
Problem 3. Consider the following the linear system . Solve the above linear system by using Gaussian elimination with partial pivoting strategy. . Solve the above linear system by using Gaussian elimination with scaled partial pivoting strategy.
Problem 3. Consider the following the linear system . Solve the above linear system by using Gaussian elimination with partial pivoting strategy. . Solve the above linear system by using Gaussian elimination with scaled partial pivoting strategy.
Linear algebra. Help with 2 and 3.
2. (21 pts.) Solve the linear system given. Write out all pivots and multipliers and write your an ordered triple. A-3 4 7| 11 3. (4 pts.) Solve the linear system given using A-1 if A=123 and Write your solution as an ordered pair.
Q1 The linear system Ax = b is given by: x1−x2 + 4x3 = 7 4x1 + 2x2 –x3= 18, x1 + 3x2+ x3 = 16, has the solution x=(3, 4,2)T. Using the initial guess x (0)=(1, 1,1)T Solve the above system as is using: Gauss-Seidel method. If the error increases, what does that mean and what should you do? (see b below) Condition the system so that convergence is secured and solve using the Gauss-Siedel method. Q2: Find a system...