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numerical analysis
QUESTION 2 Consider the linear system 21 0.52 21 + 22 23 0.2533 23...
QUESTION 2 i 0.2 -1.425 2 Consider the linear system 13 0.52 + 22 0.25.13 =...
QUESTION 2 i 0.2 -1.425 2 Consider the linear system 13 0.52 + 22 0.25.13 = Ii 0.522 + 23 whose solution is 0.9,-0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x() = (0,0,0)* as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x(0)...
QUESTION 2 Consider the linear system Ti 0.521 + 21 2 0.5x2 + 13 0.25.13 23...
QUESTION 2 Consider the linear system Ti 0.521 + 21 2 0.5x2 + 13 0.25.13 23 0.2 -1.425 2 whose solution is (0.9,-0.8, 0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x(0) - (0,0,0)' as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x(0)...
QUESTION 2 Consider the linear system 11 0.50 + Ii 22 0.579 + 23 0.2533 13...
QUESTION 2 Consider the linear system 11 0.50 + Ii 22 0.579 + 23 0.2533 13 0.2 -1.425 2 whose solution is (0.9,-0.8.0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x(0) = (0,0,0) as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w x() = (0,0,0) = 0.7 and...
QUESTION 2 Consider the linear system T 0.50 + 0.2 -1.425 12 0.5x2 + 0.25.73 23...
QUESTION 2 Consider the linear system T 0.50 + 0.2 -1.425 12 0.5x2 + 0.25.73 23 whose solution is (0.9,-0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x(0) = (0,0,0)' as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x) = (0,0,0) [20]
rx2 has 0 coefficient in the first equation QUESTION 2 Consider the linear system 11 +...
rx2 has 0 coefficient in the first equation
QUESTION 2 Consider the linear system 11 + 0.5X1 T1 12 0.5x2 + 13 0.25x3 X3 0.2 -1.425 2 = whose solution is (0.9, -0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using x(0) = (0,0,0)t as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme,...
Consider the linear system 11 0.5.01 21 + 12 0.5.22 + 13 0.25.13 13 0.2 -1.425...
Consider the linear system 11 0.5.01 21 + 12 0.5.22 + 13 0.25.13 13 0.2 -1.425 2 whose solution is (0.9,-0.8, 0.7). (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) (0) = (0,0,0)' as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x() = (0,0,0)
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficie...
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficients.
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficients.
2. Consider the following system of linear equations: -*1 + 2x2 - 13 = 2 -2:21...
2. Consider the following system of linear equations: -*1 + 2x2 - 13 = 2 -2:21 +222 + x3 = 4 3x1 + 2.02 +2.03 = 5 -3.21 + 8.22 + 5.23 = 17 (a) Put the system of linear equations into a coefficient matrix. (b) Find the reduced row echelon form of the coefficient matrix. (C) What is the dimension of the row space the coefficient matrix?
Consider the linear system 5x1 - 21 + X1 - 22 + x3 = 1 5.22...
Consider the linear system 5x1 - 21 + X1 - 22 + x3 = 1 5.22 - 23 = 2 22 5 5x3 = 3 (a) Discuss the convergence of the iterative solutions of this system generated by the Jacobi and Gauss-Seidel methods, by considering their iterative matrices. (b) If both methods converge, which one of them converges faster to the exact solution of this system? (c) Starting with the initial approximation x(0) = [0,0,0], find the number of iterations...
QUESTION 2 i 0.2 -1.425 2 Consider the linear system 13 0.52 + 22 0.25.13 = Ii 0.522 + 23 whose solution is 0.9,-0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x() = (0,0,0)* as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x(0)...
QUESTION 2 Consider the linear system Ti 0.521 + 21 2 0.5x2 + 13 0.25.13 23 0.2 -1.425 2 whose solution is (0.9,-0.8, 0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x(0) - (0,0,0)' as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x(0)...
QUESTION 2 Consider the linear system 11 0.50 + Ii 22 0.579 + 23 0.2533 13 0.2 -1.425 2 whose solution is (0.9,-0.8.0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x(0) = (0,0,0) as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w x() = (0,0,0) = 0.7 and...
QUESTION 2 Consider the linear system T 0.50 + 0.2 -1.425 12 0.5x2 + 0.25.73 23 whose solution is (0.9,-0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (5) (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) x(0) = (0,0,0)' as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x) = (0,0,0) [20]
rx2 has 0 coefficient in the first equation
QUESTION 2 Consider the linear system 11 + 0.5X1 T1 12 0.5x2 + 13 0.25x3 X3 0.2 -1.425 2 = whose solution is (0.9, -0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using x(0) = (0,0,0)t as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme,...
Consider the linear system 11 0.5.01 21 + 12 0.5.22 + 13 0.25.13 13 0.2 -1.425 2 whose solution is (0.9,-0.8, 0.7). (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using (10) (0) = (0,0,0)' as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and (5) x() = (0,0,0)
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficients.
2. Consider the following system of linear equations 23 1 Determine whether this system is consistent, and if it is, find the full set of solutions. Also, find the rank of the matrix of coefficients.
2. Consider the following system of linear equations: -*1 + 2x2 - 13 = 2 -2:21 +222 + x3 = 4 3x1 + 2.02 +2.03 = 5 -3.21 + 8.22 + 5.23 = 17 (a) Put the system of linear equations into a coefficient matrix. (b) Find the reduced row echelon form of the coefficient matrix. (C) What is the dimension of the row space the coefficient matrix?
Consider the linear system 5x1 - 21 + X1 - 22 + x3 = 1 5.22 - 23 = 2 22 5 5x3 = 3 (a) Discuss the convergence of the iterative solutions of this system generated by the Jacobi and Gauss-Seidel methods, by considering their iterative matrices. (b) If both methods converge, which one of them converges faster to the exact solution of this system? (c) Starting with the initial approximation x(0) = [0,0,0], find the number of iterations...
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