# Gaussian Elimination Count

Please help with solving the following question regarding Gaussian eliminations to a system.

The system

[see the attachment for the matrix and equation]

Where a_ij = 0 whenever i-j >= 2

Do an operation count of MD (Multiplications/Division) and AS (Addition/Subtraction) when using Gaussian elimination to solve the system.

Count [A] -> [U]

Compare the result with the count of Gaussian elimination for general matrix:

SA [A] - [U] = [see the attachment for the equation]

MD [A] -> [U] = [see the attachment for the equation]

https://brainmass.com/math/combinatorics/gaussian-elimination-count-522240

#### Solution Preview

Compare means to mention the similarities between the two answers and it also could mean to say which one is larger and why.

1. Let's start with MD:

The answer for MD: n(n+1)/2 - 1 or (n-1)(n+2)/2

For the general matrix, MD: n(n^2-1)/3

which factors to n(n+1)(n-1)/3 since n >=1 the general answer ...

#### Solution Summary

This solution provides a comparison of the operation count for different types of matrices; one matrix is general, and the other has specific elements zeroed out.