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Specificially, why is it that a human can solve a system of equations faster using Gauss elimination, yet a machine prefers cramers rule.

2006-07-20 16:14:30 · 2 answers · asked by SnowXNinja 3 in Science & Mathematics Mathematics

2 answers

I assume that when you say Gauss, you mean that you are placing the system of equations into an augmented coefficient matrix, finding the reduced row-echelon form (rref) of the matrix, then viewing your answers.

The reason is that, with practice, you can find the rref of an augmented matrix quite quickly. Then, the answers are obvious. For example, if you come up with a rref matrix as follows:
1 0 0 | 3
0 1 0 | 4
0 0 1 | 5
Then you know that x = 3, y = 4, and z = 5.

However, for a computer to find the rref of a matrix, it must do the calculations that you do for rref, but it also has to follow the logic that you follow. The program for this logic is actually a long program.

With Cramer's rule, however, if a computer has the coefficients of the equations, along with the constant value at the end, it can first find the determinant of the coefficient matrix, then substitute the constants into the appropriate column of the coefficient matrix for each row, find the determinants of the new matrix, then divide for each solution in the set. This is a longer process for humans.

2006-07-20 16:34:34 · answer #1 · answered by Anonymous · 3 0

Were did you read that Cramer is more efficient than Gauss ?

http://ceee.rice.edu/Books/LA/diff/diff2.html

Cramers rule is never used in solving a set of equations. It is inferior to Gauss in terms of stability and performance. It is basicly used for proofs for instance that a set of equations has a solution.

2006-07-21 01:12:48 · answer #2 · answered by gjmb1960 7 · 0 0

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