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leezysosteezy leezysosteezy
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11 years ago
Both Gaussian Elimination and cramers rule are used to solve linear systems. If you need to solve large systems with more than three variables, which is more efficient and why?
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Rinoa92Rinoa92
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11 years ago
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11 years ago
obviously Gaussian Elimination suits large systems and can be programmed easily or the codes are available
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11 years ago
Gaussian elimination takes a number of operations proportional to the cube of the number of variables and equations. Cramer's rule requires finding the determinant - the ordinary technique of expansion by minors takes time proportional to the factorial of the number of variables and equations, so it is much slower for large systems. The answer is Gaussian elimination.

Note that you can use Gaussian elimination to find determinants also. However, since Cramer's rule requires finding N+1 determinants, it is more efficient just to do Gaussian elimination once.
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