Question: Gaussian elimination, the classic algorithm for solving systems of n linear equations in n unknowns, requires about 1/3*n^3 multiplications, which is the algorithm's basic

Gaussian elimination, the classic algorithm for solving systems of n linear equations

Gaussian elimination, the classic algorithm for solving systems of n linear equations in n unknowns, requires about 1/3*n^3 multiplications, which is the algorithm's basic operation. a. [20 points] How much longer should you expect Gaussian elimination to work on a system of 1000 equations versus a system of 500 equations? b. [30 points] You are considering buying a computer that is 1000 times faster than the one you currently have. By what factor will the faster computer in- crease the sizes of systems solvable in the same amount of time as on the old computer?

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