Question

Solve the following systems using Jacobi method :- 5x-2y+3z=-1 (a) -3x+9y+z=2 2x-y-7z=3. 2x-y=7 (b) -x+2y-z=1 -y-2z=1. 7x-2y+z=17 (c) x-9y+3z-w=13 2x+10z+w=15 x-y+z+6w=10 Solve the following system using Gauss-Seidel method - (a) 7x-2y+z,=17 x-9y+3z-w,=13 2x+10z+w,=15 x-y+z+6w,=10 4x+y+z,=2 (b) x+5y+2z=-6 x+2y+3z,=-4. Solve the above system in question 2 by SOR method with omega =1.12. Determine the rate of convergence of the Jacobi method and Gauss-Seidel method for the system: - 4x+0y+2z=4 0x+5y+2z=-3 5x+4y+10z=2. (a) 0x+5y+2z=-3 5x+4y+10z=2. (b) 3x+y+z=4 -2x+4y+0z=1 -x+2y-6z=2 Given the matrix A=I+L+U where A=[[1,2,-2],[1,1,1],[2,2,1]],L and U are strictly lower and upper triangular matrix respectively, decide whether Jacobi and Gauss Seidel method converge to Ax=b. Given the matrix A=D+L+U where A=[[3,1,1],[-2,4,0],[-1,2,6]],L and U are strictly lower and upper triangular matrix respectively, decide whether Jacobi and Gauss Seidel method converge to Ax=b. The system of equations Ax=b is to be solved iteratively by x_(n+1)=Hx_(n)+b suppose A=[[1,k],[2k,1]],k!=(sqrt(2))/(2),k real Find a necessary and sufficient condition on k for convergence of Jacobi method. 3x+y+z=4 8. Given the system -2x+4y+0z=1 this system can be solved by the relaxation method. Write down the iteration formula exactly. 9. Solve the system of equations 4x+y+z=2 x+5y+2z=-6 x+2y+3z=-4. using Jacobi iteration method and find it in error format. Take initial guess as x^(0)=[0.5,-0.5-0.5]^(T) and perform three iterations in each case. Same as do for Gauss Seidel method. 5-2y+3 -1 (a) 3r+9y+ z = 2 2 - y - 7z - 3. fi - 7 (b) + 2y - 2 y = 2: - 1. 7x 2y + = 17 =9y+3=w = 13 (e) 2x+10+w 15 -y++6 = 10 2. Solve the following system using Gauss-Seidel method - 7x 2y + z = 17 = 9y + 3z = w 13 (a) 2 + 10z + w = 15 -y++6 = 10 4x + y + : = 2 (b) +5y+2z 6 + 2y+ 3z = 4. 3. Solve the above system in question 2 by SOR method with = 1.12 4. Determine the rate of convergence of the Jacobi method and Gauss-Seidel method for the system: - 4x + 0y + 2: = 4 (a) 0x +5y+ 2z - 3 5 + 4y + 10z = 2. 3 + y + : = 4 (b) 2x +4y+0 = - r+ 2y - 6z = 5.Given the matrix A=I+L+U where A=111 , L and U are strictly lower and upper triangular matrix respectively [22 decide whether Jacobi and Gauss Seidel method converge to Ax = b 3 6. Given the matrix A = D + L + U where A = 0 L and U are strictly lower and upper triangular matrix -1 respectively, decide whether Jacobi and Gauss Seidel method converge to Ar = b. 7. The system of equations Ar = b is to be solved iteratively by n+1=Hx+b suppose A = Find a necessary and sufficient condition on k for convergence of Jacobi method. 3 +y + : = 8. Given the system -2x+4y+0z = 1 this system can be solved by the relaxation method. Write down the iteration + 2y 6z = 2. formula exactly. 9. Solve the system of equations 4x + y + : +5y+2=-6 +2y+3z=4. using Jacobi iteration method and find it in error format. Take initial guess as = [0.5, 0.5 0.5]7 and perform three iterations in each case. Same as do for Gauss Seidel method.

          Solve the following systems using Jacobi method :-
5x-2y+3z=-1
(a) -3x+9y+z=2
2x-y-7z=3.
2x-y=7
(b) -x+2y-z=1
-y-2z=1.
7x-2y+z=17
(c)
x-9y+3z-w=13
2x+10z+w=15
x-y+z+6w=10
Solve the following system using Gauss-Seidel method -
(a)
7x-2y+z,=17
x-9y+3z-w,=13
2x+10z+w,=15
x-y+z+6w,=10
4x+y+z,=2
 (b) x+5y+2z=-6
x+2y+3z,=-4.
Solve the above system in question 2 by SOR method with omega =1.12.
Determine the rate of convergence of the Jacobi method and Gauss-Seidel method for the system: -
4x+0y+2z=4
0x+5y+2z=-3
5x+4y+10z=2.
(a)
0x+5y+2z=-3
5x+4y+10z=2.
(b)
3x+y+z=4
-2x+4y+0z=1
-x+2y-6z=2
Given the matrix A=I+L+U where A=[[1,2,-2],[1,1,1],[2,2,1]],L and U are strictly lower and upper triangular matrix respectively, decide whether Jacobi and Gauss Seidel method converge to Ax=b.
Given the matrix A=D+L+U where A=[[3,1,1],[-2,4,0],[-1,2,6]],L and U are strictly lower and upper triangular matrix respectively, decide whether Jacobi and Gauss Seidel method converge to Ax=b.
The system of equations Ax=b is to be solved iteratively by
x_(n+1)=Hx_(n)+b
suppose A=[[1,k],[2k,1]],k!=(sqrt(2))/(2),k real
Find a necessary and sufficient condition on k for convergence of Jacobi method.
3x+y+z=4
8. Given the system -2x+4y+0z=1 this system can be solved by the relaxation method. Write down the iteration formula exactly.
9. Solve the system of equations
4x+y+z=2
x+5y+2z=-6
x+2y+3z=-4.
using Jacobi iteration method and find it in error format. Take initial guess as x^(0)=[0.5,-0.5-0.5]^(T) and perform three iterations in each case. Same as do for Gauss Seidel method.
5-2y+3 -1 (a) 3r+9y+ z = 2 2 - y - 7z - 3. fi - 7 (b)  + 2y - 2 y = 2: - 1. 7x  2y +  = 17 =9y+3=w = 13 (e) 2x+10+w 15  -y++6 = 10
2. Solve the following system using Gauss-Seidel method - 7x  2y + z = 17  = 9y + 3z = w 13 (a) 2 + 10z + w = 15 -y++6 = 10 4x + y + : = 2 (b)  +5y+2z 6 + 2y+ 3z = 4.
3. Solve the above system in question 2 by SOR method with  = 1.12
4. Determine the rate of convergence of the Jacobi method and Gauss-Seidel method for the system: - 4x + 0y + 2: = 4 (a) 0x +5y+ 2z - 3 5 + 4y + 10z = 2.
3 + y + : = 4 (b) 2x +4y+0 = - r+ 2y - 6z =
5.Given the matrix A=I+L+U where A=111 , L and U are strictly lower and upper triangular matrix respectively [22 decide whether Jacobi and Gauss Seidel method converge to Ax = b
3 6. Given the matrix A = D + L + U where A = 0 L and U are strictly lower and upper triangular matrix -1 respectively, decide whether Jacobi and Gauss Seidel method converge to Ar = b.
7. The system of equations Ar = b is to be solved iteratively by
n+1=Hx+b
suppose A =
Find a necessary and sufficient condition on k for convergence of Jacobi method. 3 +y + : = 8. Given the system -2x+4y+0z = 1 this system can be solved by the relaxation method. Write down the iteration  + 2y  6z = 2. formula exactly.
9. Solve the system of equations 4x + y + : +5y+2=-6 +2y+3z=4. using Jacobi iteration method and find it in error format. Take initial guess as  = [0.5, 0.5  0.5]7 and perform three iterations in each case. Same as do for Gauss Seidel method.

solve the following systems using jacobi method 5x 2y3z 1 a 3x9yz2 2x y 7z3 2x y7 b x2y z1 y 2z1 7x 2yz17 c x 9y3z w13 2x10zw15 x yz6w10 solve the following system using gauss seidel method 62504

Added by Nicole E.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

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To solve the given systems using the Jacobi and Gauss-Seidel methods, follow these steps: ### Jacobi Method #### System (a) Show more…

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Solve the following systems using Jacobi method :- 5x-2y+3z=-1 (a) -3x+9y+z=2 2x-y-7z=3. 2x-y=7 (b) -x+2y-z=1 -y-2z=1. 7x-2y+z=17 (c) x-9y+3z-w=13 2x+10z+w=15 x-y+z+6w=10 Solve the following system using Gauss-Seidel method - (a) 7x-2y+z,=17 x-9y+3z-w,=13 2x+10z+w,=15 x-y+z+6w,=10 4x+y+z,=2 (b) x+5y+2z=-6 x+2y+3z,=-4. Solve the above system in question 2 by SOR method with omega =1.12. Determine the rate of convergence of the Jacobi method and Gauss-Seidel method for the system: - 4x+0y+2z=4 0x+5y+2z=-3 5x+4y+10z=2. (a) 0x+5y+2z=-3 5x+4y+10z=2. (b) 3x+y+z=4 -2x+4y+0z=1 -x+2y-6z=2 Given the matrix A=I+L+U where A=[[1,2,-2],[1,1,1],[2,2,1]],L and U are strictly lower and upper triangular matrix respectively, decide whether Jacobi and Gauss Seidel method converge to Ax=b. Given the matrix A=D+L+U where A=[[3,1,1],[-2,4,0],[-1,2,6]],L and U are strictly lower and upper triangular matrix respectively, decide whether Jacobi and Gauss Seidel method converge to Ax=b. The system of equations Ax=b is to be solved iteratively by x_(n+1)=Hx_(n)+b suppose A=[[1,k],[2k,1]],k!=(sqrt(2))/(2),k real Find a necessary and sufficient condition on k for convergence of Jacobi method. 3x+y+z=4 8. Given the system -2x+4y+0z=1 this system can be solved by the relaxation method. Write down the iteration formula exactly. 9. Solve the system of equations 4x+y+z=2 x+5y+2z=-6 x+2y+3z=-4. using Jacobi iteration method and find it in error format. Take initial guess as x^(0)=[0.5,-0.5-0.5]^(T) and perform three iterations in each case. Same as do for Gauss Seidel method. 5-2y+3 -1 (a) 3r+9y+ z = 2 2 - y - 7z - 3. fi - 7 (b) + 2y - 2 y = 2: - 1. 7x 2y + = 17 =9y+3=w = 13 (e) 2x+10+w 15 -y++6 = 10 2. Solve the following system using Gauss-Seidel method - 7x 2y + z = 17 = 9y + 3z = w 13 (a) 2 + 10z + w = 15 -y++6 = 10 4x + y + : = 2 (b) +5y+2z 6 + 2y+ 3z = 4. 3. Solve the above system in question 2 by SOR method with = 1.12 4. Determine the rate of convergence of the Jacobi method and Gauss-Seidel method for the system: - 4x + 0y + 2: = 4 (a) 0x +5y+ 2z - 3 5 + 4y + 10z = 2. 3 + y + : = 4 (b) 2x +4y+0 = - r+ 2y - 6z = 5.Given the matrix A=I+L+U where A=111 , L and U are strictly lower and upper triangular matrix respectively [22 decide whether Jacobi and Gauss Seidel method converge to Ax = b 3 6. Given the matrix A = D + L + U where A = 0 L and U are strictly lower and upper triangular matrix -1 respectively, decide whether Jacobi and Gauss Seidel method converge to Ar = b. 7. The system of equations Ar = b is to be solved iteratively by n+1=Hx+b suppose A = Find a necessary and sufficient condition on k for convergence of Jacobi method. 3 +y + : = 8. Given the system -2x+4y+0z = 1 this system can be solved by the relaxation method. Write down the iteration + 2y 6z = 2. formula exactly. 9. Solve the system of equations 4x + y + : +5y+2=-6 +2y+3z=4. using Jacobi iteration method and find it in error format. Take initial guess as = [0.5, 0.5 0.5]7 and perform three iterations in each case. Same as do for Gauss Seidel method.