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# who else finds Cramer's Rule useless? Watch

1. I would never use it to solve linear equations. I prefer Gaussian or even do row operations manually (without putting them in matrices)
2. (Original post by reyjusuf)
I would never use it to solve linear equations. I prefer Gaussian or even do row operations manually (without putting them in matrices)
Cramer's rule is actually the method that I learnt first. I must say that inverting the matrix using Gaussian Elimination or otherwise seems so much tidier, but I guess with Cramer's rule you can just plug numbers into a calculator.
I imagine that computing a few determinants with a computer is probably quicker, but I don't know
3. (Original post by joostan)
Cramer's rule is actually the method that I learnt first. I must say that inverting the matrix using Gaussian Elimination or otherwise seems so much tidier, but I guess with Cramer's rule you can just plug numbers into a calculator.
I imagine that computing a few determinants with a computer is probably quicker, but I don't know
I believe solving by Gaussian elimination and calculating a determinant are both O(n^3) operations (at least for fairly standard algorithms, you may be able to do better for large n using some kind of divide and conquer).

Since Cramer's rule requires n determinants, it would therefore be O(n^4) and slower than Gaussian elimination.

For n > 2 the only thing Cramer's rule really has going for it is conciseness of notation, to be honest.
4. (Original post by DFranklin)
I believe solving by Gaussian elimination and calculating a determinant are both O(n^3) operations (at least for fairly standard algorithms, you may be able to do better for large n using some kind of divide and conquer).

Since Cramer's rule requires n determinants, it would therefore be O(n^4) and slower than Gaussian elimination.

For n > 2 the only thing Cramer's rule really has going for it is conciseness of notation, to be honest.
That's fair enough, though I was thinking of using a calculator or something similar which can compute a determinant. Mind you it can solve simultaneous equations too.
5. Calculators almost certainly compute determinants using Gaussian elimination as well.
6. (Original post by reyjusuf)
I would never use it to solve linear equations. I prefer Gaussian or even do row operations manually (without putting them in matrices)
It can be useful for proving stuff, but that's really quite rare, since Gaussian elimination lets you use induction.
7. (Original post by DFranklin)
Since Cramer's rule requires n determinants, it would therefore be O(n^4) and slower than Gaussian elimination.
Not directly relevant to the OP but apparently Cramer's rule can be implemented in O(n3)
8. (Original post by LogicGoat)
Not directly relevant to the OP but apparently Cramer's rule can be implemented in O(n3)
Not exactly a "standard algorithm" though. (It's also "divide and conquer" as I alluded).

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