Gauss Elimination Method MCQ Quiz in हिन्दी - Objective Question with Answer for Gauss Elimination Method - मुफ्त [PDF] डाउनलोड करें

Concept:

Gauss-Seidel Method:

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

2x - 5y + z = 8

Putting y = 0, z = 0 ⇒ x = 4

x + 3y - 2z = 6

Putting x = 4, z = 0 ⇒ y = 0.6

3x + 2y + z = 9

Putting x = 4, y = 0.6 ⇒ z = 9 – 3 x 4 – 2(0.6)

z = - 4.2

Mistake Point:

Don’t arrange them diagonally because It is given in question solve as per given order.

Explanation:

Equation are

20x + y – 2z = 17

3x + 20y – z = -18

2x – 3y + 20z = 25

Re-writing the above equations.

$x=\frac{1}{20}\left(17-y+2z\right)$         ---(1)

$y=\frac{1}{20}\left(-18-3x+z\right)$        ---(2)

$z=\frac{1}{20}\left(25-2x+3y\right)$          ---(3)

Putting y0 = z0 = 0 in equation (1)

$x_1=\frac{1}{20}\left(17-0+0\right)$

∴ x₁ = 0.85

Putting x = 0.85, z = 0 in equation (2)

$y_1=\frac{1}{20}\left(-18-\left(3\times 0.85\right)+0\right)$

∴ y₁ = - 1.0275

Putting x = 0.85, y = -1.0275 in eq. (3)

$z_1=\frac{1}{20}\left[25-\left(2\times 0.85\right)+3\left(-1.0275\right)\right]$

∴ z₁ = 1.010875

व्याख्या:

समीकरण हैं:

20x + y - 2z = 17

3x + 20y - z = -18

2x - 3y + 20z = 25

ऊपर दिए गए समीकरणों को पुनः लिखने पर:

$x=\frac{1}{20}\left(17-y+2z\right)$ ---(1)

$y=\frac{1}{20}\left(-18-3x+z\right)$ ---(2)

$z=\frac{1}{20}\left(25-2x+3y\right)$ ---(3)

समीकरण (1) में y₀ = z₀ = 0 रखने पर:

$x_1=\frac{1}{20}\left(17-0+0\right)$

इसलिए x₁ = 0.85

समीकरण (2) में x = 0.85, z = 0 रखने पर:

$y_1=\frac{1}{20}\left(-18-\left(3\times 0.85\right)+0\right)$

इसलिए y₁ = -1.0275

समीकरण (3) में x = 0.85, y = -1.0275 रखने पर:

$z_1=\frac{1}{20}\left[25-\left(2\times 0.85\right)+3\left(-1.0275\right)\right]$

इसलिए z₁ = 1.010875

व्याख्या:

समीकरण हैं:

20x + y - 2z = 17

3x + 20y - z = -18

2x - 3y + 20z = 25

ऊपर दिए गए समीकरणों को पुनः लिखने पर:

$x=\frac{1}{20}\left(17-y+2z\right)$ ---(1)

$y=\frac{1}{20}\left(-18-3x+z\right)$ ---(2)

$z=\frac{1}{20}\left(25-2x+3y\right)$ ---(3)

समीकरण (1) में y₀ = z₀ = 0 रखने पर:

$x_1=\frac{1}{20}\left(17-0+0\right)$

इसलिए x₁ = 0.85

समीकरण (2) में x = 0.85, z = 0 रखने पर:

$y_1=\frac{1}{20}\left(-18-\left(3\times 0.85\right)+0\right)$

इसलिए y₁ = -1.0275

समीकरण (3) में x = 0.85, y = -1.0275 रखने पर:

$z_1=\frac{1}{20}\left[25-\left(2\times 0.85\right)+3\left(-1.0275\right)\right]$

इसलिए z₁ = 1.010875

Explanation:

Equation are

20x + y – 2z = 17

3x + 20y – z = -18

2x – 3y + 20z = 25

Re-writing the above equations.

$x=\frac{1}{20}\left(17-y+2z\right)$         ---(1)

$y=\frac{1}{20}\left(-18-3x+z\right)$        ---(2)

$z=\frac{1}{20}\left(25-2x+3y\right)$          ---(3)

Putting y0 = z0 = 0 in equation (1)

$x_1=\frac{1}{20}\left(17-0+0\right)$

∴ x₁ = 0.85

Putting x = 0.85, z = 0 in equation (2)

$y_1=\frac{1}{20}\left(-18-\left(3\times 0.85\right)+0\right)$

∴ y₁ = - 1.0275

Putting x = 0.85, y = -1.0275 in eq. (3)

$z_1=\frac{1}{20}\left[25-\left(2\times 0.85\right)+3\left(-1.0275\right)\right]$

∴ z₁ = 1.010875

Concept:

Gauss-Seidel Method:

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

2x - 5y + z = 8

Putting y = 0, z = 0 ⇒ x = 4

x + 3y - 2z = 6

Putting x = 4, z = 0 ⇒ y = 0.6

3x + 2y + z = 9

Putting x = 4, y = 0.6 ⇒ z = 9 – 3 x 4 – 2(0.6)

z = - 4.2

Mistake Point:

Don’t arrange them diagonally because It is given in question solve as per given order.