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

Gaussian elimination, the classic algorithm for solving systems of n linear equations in n unknowns, requires about multiplications, which is the algorithm’s basic operation.

a. How much longer should you expect Gaussian elimination to work on a system of 1000 equations versus a system of 500 equations?

b. You are considering buying a computer that is 1000 times faster than the one you currently have. By what factor will the faster computer increase the sizes of systems solvable in the same amount of time as on the old computer?