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Bsc CSIT Semester 3 – Numerical Method – Unit 4: Solving System of Linear Equations (8 Hrs.)

Comprehensive questions and detailed answers for Unit 4: Solving System of Linear Equations (8 Hrs.). Perfect for exam preparation and concept clarity.

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What are the limitations of direct methods for solving a system of linear equations? How Gauss Seidel method differs from Jacobi iteration? Solve the following system of linear equation using Jacobi iteration method.

\quad \quad \quad \quad 2x-7y-10z=-17\\ \quad \quad \quad \quad 5x+y+3z=14\\ \quad \quad \quad \quad x+10y+9z=7

MediumNumerical10 marks2081(TU Final)

Solve the following system of linear equations using Gauss-Jordan elimination method.

$x+2y-3z=4 2x+4y-6z=8 x-2y+5z=4$

MediumNumerical5 marks2081(TU Final)

How Gauss Jordan method differs from Gauss Elimination method? Solve the following system of equations using Gauss Jordan method. How can we use Gauss Jordan method to find the inverse of a matrix? Discuss.

$2x - y + 4z = 15\\ 2x + 3y - 2z = 4\\ 3x + 2y - 4z = -4$

HardNumerical10 marks2080(TU Final)

Factorise the following matrix using Cholesky method.

\begin{bmatrix} 2 & 1 & 1\\ 3 & 2 & 3\\ 1 & 4 & 9 \end{bmatrix}

MediumNumerical5 marks2080(TU Final)

What is pivoting? Why is it necessary? Write an algorithm and program to solve the set of n linear equations using Gaussian elimination method.

HardNumerical10 marks2079(TU Final)

Solve the following set of equations using Gauss Siedal method.

$x + 2y + 3z = 4\\ 6x + 4y + 5z = 16\\ 5x + 2y + 3z = 12$

MediumNumerical5 marks2079(TU Final)

Write matrix factorization? How can be used to solve a system of linear equations? Factorize the given matrix A and solve the system of equations Ax = b for given b using L and U matrices.

A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 8 & 11\\ 3 & 22 & 36 \end{bmatrix} \text{and } b = \begin{bmatrix} 4\\ 12\\ 28 \end{bmatrix}

HardNumerical10 marks2078(TU Final)

Why partial pivoting is used with Naive Gauss Elimination method? Solve the following system of equations using Gauss Elimination method with partial pivoting? How Gauss Jordan method differs from Gauss elimination method?

\begin{aligned} 2x + 2y - z &= 6 \\ 4x + 2y + 3z &= 4 \\ x + y + z &= 0 \end{aligned}

HardNumerical10 marks2077(TU Final)

Discuss the Doolittle LU decomposition method for matrix factorization.

MediumNumerical5 marks2077(TU Final)

Solve the following set of linear equations using the Gauss-Jordan method.

$x2 + 2x3 + 3x4 = 9\\ 7x1 + 6x2 + 5x3 + 4x4 = 33\\ 8x1 + 9x2 + x4 = 27\\ 2x1 + 5x2 + 4x3 + 3x4 = 23$

MediumNumerical5 marks2078(TU Final)

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What are the limitations of direct methods for solving a system of linear equations? How Gauss Seidel method differs from Jacobi iteration? Solve the following system of linear equation using Jacobi i

Marks: 10Chapter: Unit 4: Solving System of Linear Equations (8 Hrs.)

Solve the following system of linear equations using Gauss-Jordan elimination method. \[ x+2y-3z=4 2x+4y-6z=8 x-2y+5z=4 \]

Marks: 5Chapter: Unit 4: Solving System of Linear Equations (8 Hrs.)

How Gauss Jordan method differs from Gauss Elimination method? Solve the following system of equations using Gauss Jordan method. How can we use Gauss Jordan method to find the inverse of a matrix? Di

Marks: 10Chapter: Unit 4: Solving System of Linear Equations (8 Hrs.)

Factorise the following matrix using Cholesky method. \[ \begin{bmatrix} 2 & 1 & 1\\ 3 & 2 & 3\\ 1 & 4 & 9 \end{bmatrix} \]

Marks: 5Chapter: Unit 4: Solving System of Linear Equations (8 Hrs.)

What is pivoting? Why is it necessary? Write an algorithm and program to solve the set of n linear equations using Gaussian elimination method.

Marks: 10Chapter: Unit 4: Solving System of Linear Equations (8 Hrs.)

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