Question
Download Solution PDFThe 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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 = 0 ⇒ y = - 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
Last updated on May 26, 2025
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