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- Compute the matrix exponential e^At for the system x′=Ax given below. x′1=20x1−20x2, x′2=10x1−10x2 eAt=enter your response hereFor a linear algebra matrix with initial value, how would I set up a general formula for xk to determine the limit as k approaches infinity for xk?Suppose that all the eigenvalues of the matrix A have negative real part. Then everysolution of the differential equation x`= Ax satisfies,|x(t)| ≤ |x(s)|, if t > s.
- If A is a 3x3 matrix with eigenvalues 0,3,2 and corresponding eigenvectors u,v,w, then the linear system Ax = 3v+2w has infinitely many solutions. Is this statement True or False?solve for w,x,y,z using Gaussian eliminationThe coefficient matrix is not strictly diagonally dominant, nor can the equations be rearranged to make it so. However, both the Jacobi and the Gauss-Seidel method converge anyway. Demonstrate that this is true of the Gauss-Seidel method, starting with the zero vector as the initial approximation and obtaining a solution that is accurate to within 0.01.