The approximate solution of the system of simultaneous equations

2x - 5y + 3z = 7

x + 4y - 2z = 3

2x + 3y + z = 2

by applying Gauss-Seidel method one time (using initial approximation as x - 0, y - 0, z - 0) will be:

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  1. x = 2.32, y = 1.245, z = -3.157
  2. x = 1.25, y = -2.573, z = -3.135
  3. x = 2.45, y = -1.725, z = -3.565
  4. x = 3.5, y = -0.125, z = -4.625

Answer (Detailed Solution Below)

Option 4 : x = 3.5, y = -0.125, z = -4.625
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Detailed Solution

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Concept:

Gauss Seidel Method:

In Gauss Seidel method, the value of x calculated is used in next calculation putting other variable as 0.

2x - 5y + 3z = 7

Putting y = 0, z = 0 ⇒ x = 3.5

x + 4y - 2z = 3

Putting x = 3.5, z = 0y = - 0.125

2x + 3y + z = 2

Putting x = 3.5, y = - 0.125 ⇒ z = 2 – 3(-0.125) – 2(3.5)

z = - 4.625

Hence, The approximate solution of the system of simultaneous equations is x = 3.5, y = -0.125, z = -4.625

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