Gaussian Elimination Count
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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]
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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.
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 ...
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