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# Solve Using Gauss Jacobi Iteration Method 2𝒙 + 12y + Z – 4w = 13 13𝒙 + 5y - 3z + W = 18 2𝒙 + Y – 3z + 9w = 31 3𝒙 - 4y + 10z + W = 29 - Applied Mathematics 1

Sum

Solve using Gauss Jacobi Iteration method
2𝒙 + 12y + z – 4w = 13
13𝒙 + 5y - 3z + w = 18
2𝒙 + y – 3z + 9w = 31
3𝒙 - 4y + 10z + w = 29

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#### Solution

x=(18-5y+3z-w)

y=(13-2x-z+4w)

z=(29-3x+4y-w)

w=(31-2x-y+3z)/9

 Iteration x y z w 1 1.3846 1.0833 2.9 3.4444 2 1.3722 1.7590 2.5735 3.9831 3 0.9956 1.9679 2.7936 3.8019 4 0.9800 1.9519 3.0083 3.9357 5 1.0254 1.9812 2.9932 4.0126 6 1.0047 2.0005 2.9836 3.9942 7 0.9965 1.9987 2.9994 8 1.0009 1.9984 3.0012 9 1.0008 2.0000 2.9990 10 0.9997 2.0001 2.9997 11 0.9999 1.9999 3.0002 12 1.0001 2 3 13 1 2 3

∴ x = 1, y = 2, z = 3, w = 4.

Concept: Gauss Jacobi Iteration Method
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