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- Thread starter Zythyr
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http://tutorial.math.lamar.edu/Classes/LinAlg/DeterminantByRowReduction.aspx

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Defennder

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It's going to be quite tedious even if you were to row-reduce it before finding its determinant. Some special matrices have easy determinants, so maybe you could see if the matrix for which you are trying to evaluate the determinant has some property which allows you to compute its determinant easily.

EDIT: I see that you say you are trying to "figure out the formula". There's a recursive method for finding the determinants of an arbitrary nxn matrix. It's known as cofactor expansion.

EDIT: I see that you say you are trying to "figure out the formula". There's a recursive method for finding the determinants of an arbitrary nxn matrix. It's known as cofactor expansion.

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Borek

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I know that's not what you are asking for, but in the case of 10x10... go numerical.

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"Cofactor expansion" or "Laplace expansion"

http://tutorial.math.lamar.edu/Classes/LinAlg/MethodOfCofactors.aspx (has 5x5 example)

http://en.wikipedia.org/wiki/Expansion_by_minors

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Haelfix

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You are almost guarenteed to make an algebra error somewhere. This is exactly what computers are for.

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Defennder

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Is this question from a textbook? If so, then perhaps it's best if you were to post the exact problem. The problem with devising a formula for the determinant of a 10x10 matrix is that it would require far too many variables, at least 100 variables would be needed, each for every entry of the matrix. I doubt any textbook problem would require such to be done.

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Not in a textbook. My proffesor for Diffiq said if anyone figures out the forumal for the dertminant of a 10x10, they automatically get an A in the class.Is this question from a textbook? If so, then perhaps it's best if you were to post the exact problem. The problem with devising a formula for the determinant of a 10x10 matrix is that it would require far too many variables, at least 100 variables would be needed, each for every entry of the matrix. I doubt any textbook problem would require such to be done.

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Defennder

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with(LinearAlgebra); M:=Matrix(3,3,symbol=m); Determinant(M);

You might wish gradually tune the size of the square matrix up to your desired value... but you should be prepared to wait.

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I doubt that your professor would actually give an A for it though since it is extremely easy.

Hell, I wonder if this would suffice: (Let [tex]a_{i,j}[/tex] denote the i,jth entry of the matrix)

[tex]\sum_{\sigma \in S_{10}} \text{sgn}(\sigma) \sum_{i=1}^{10} a_{i, \sigma(i)}[/tex]

because that is one way to write the formula. It's called Leibniz's formula for the determinant. Of course you'd need to know what [tex]S_{10}[/tex] is and what the sign of an element of [tex]S_{10}[/tex] means as well as how to interpret the summation signs