Learn Gaussian Elimination

Introduction to learn Gaussian elimination:

In linear algebra, Learning Gaussian elimination is an algorithm for solving systems of linear equations, finding the rank of a matrix, and calculating the inverse of an invertible square matrix. Gaussian elimination is named after German mathematician and scientist Carl Friedrich Gauss.

Elementary row operations are used to reduce a matrix to row echelon form. Gauss–Jordan elimination, an extension of this algorithm, reduces the matrix further to reduced row echelon form. Gaussian elimination alone is sufficient for many applications.

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Solving by Learning Gaussian Elimination:


A technique of solve a method of n linear equations in a n unknowns, in which there are first n - 1 steps, the math step of which consists of subtracting a lots of the math equation from both of the pursue ones so as to remove one variable, ensuing in a triangular set of equations which can be solved by turn around substitution, compute the nth variable from the nth equation, the (n-1)st variable from the (n-1)st equation.

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Example problems for learning Gaussian Elimination:


Example problems for learning Gaussian Elimination are as follows:

1) Solve the following system equation using Gaussian Elimination method.

3x + y = 9

3x – y = 15

Solution:

If add down, the y determination cancel out. So sketch an "equals" bar below the system, and add down:

3x + y = 9

3x – y = 15

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6x = 24

x = 24 / 6

x = 4

At the present divide from side to side to solve for x = 4, and then back-solve, using either of the original equations, to find the value of y. The first equation have lesser facts, so back - explain in that one:

2(4) + y = 10

8 + y = 10

y = 2

Then the solution is (x, y) = (4, 2)

2) Solve the following system using Elimination method.

2x + 2y = 4 --- (1)

4x – 3y = 8 ---- (2)

Solution:

Multiply equation 1 with (3) and multiply equation, 2 with (2)

6x + 6y = 12

8x – 6y = 16

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14x = 28

x = 28/14

x = 2

Apply x=2 in equation (1)

2(2) +2 y = 4

4 + 2y = 4

2y = 4 -4

y=0

Then the solution is (x, y) = (2, 0).