Introduction..., Implementation in c++......, Output..., Advantages and Disadvantages....., and Application.

1. MATHEMATICS PRESENTATION
GAUSS ELEMINATION METHOD

2. CARL FRIEDRICH GAUSS
THE PRINCE OF MATHEMATICS
• Son of a gardner
• Encouraged by mother and uncle

3. • Arithmetic progression
• Carl Ferdinand
• Heptadecagon(17)
• Proof for algebraic equations
• Crown prime

4. GAUSS ELEMINATION METHOD
• Row reduction method
• Elementary row transformation
Swapping two rows
Multiplying a row by a non zero number
Adding a multiple of one row to another
• Leading coefficients
• Backward substitution

6. PIVOTISATION

7. GAUSS ELEMINATION

8. BACKWARD SUBSTITUTION

9. SOLUTION FOR GIVEN EQUATION

10. ADVANTAGES
• It is the direct method for solving linear
simultaneous equation.
• The complexity involved is of the order O(n^3)
which is very low when compared to other
methods.

11. DISADVANTAGES
• Divisible by zero during pivoyization
• Round off errors – as one result depends on
previous result
• it involves in backward substitution if any of the
previous result is wrong then all the forth
coming result becomes wrong.
• Ill conditioned system-small change in
coefficient, large change in solution.

12. APPLICATIONS
• Computing ranks
Since Gauss elimination method results in
row echolen form using that we can find rank of
the matrix
• Generalisation
It can be performed over several fields
not just real numbers
• Computational efficiency
It can be used to find the computational
efficiency by measuring the no of arithmetic
operations required to perform row reduction

13. QUOTES
• GOD DO ARITHMETIC
• You have no idea, how much poetry there is in
the calculation of a table of logarithms!
• Ask her to wait a moment I am almost done.