Gauss Elimination

Provide an example of a system of equations that can be solved using Gauss Elimination.

• 2x + 3y = 5, 4x + y = 11

• 6x + 3y = 12, 2x - 5y = 1

• x - 4y = 8, 2x + 2y = 10

• 3x + 2y = 7, 5x - y = 3

What is the computational complexity of the Gauss Elimination method?

• O(log n)

• O(n^4)

• O(n^3)

• O(n^2)

What are some common pitfalls to avoid when using Gauss Elimination?

• Using random pivoting techniques

• Always performing back substitution first

• Avoiding pivoting, zero pivots, inadequate scaling, incorrect order of operations, and neglecting back substitution.

• Ignoring the need for matrix normalization

Solve the given system of equation by Gaussian Elimination method.

3x + 4y – z = -6

-2y + 10z = -8

4y – 2z = -2

• (-2, -1, -1)

• (-1, -2, -1)

• (-1, -1, -2)

• (-1, -1, -1)

The aim of elimination steps in Gaussian elimination method is to reduce the coefficient matrix to ____________

• diagonal

• identity

• lower triangular

• upper triangular

In Gaussian elimination method, original equations are transformed by using _____________

• Column operations

• Row Operations

• Mathematical Operations

• Subset Operation

The Elimination process in Gauss Elimination method is also known as _____________

• Forward Elimination

• Backward Elimination

• Sideways Elimination

• Crossways Elimination

The reduced form of the Matrix in Gaussian Elimination method is also called ____________

• Column Echelon Form

• Row-Column Echelon Form

• Column-Row Echelon Form

• Row Echelon Form

Gaussian elimination is a name given to a well known method of solving simultaneous equation by successively eliminating _________

• Variables

• Equations

• Unknown

• Algorithms

Solve the following equations by Gaussian Elimination Method.

• x = 7, y = -3 , z = -2

• x = -7, y = -3 , z = -2

• x = -3, y = -7 , z = -2

• x = -2, y = -3 , z = -7