Is there any tool to solve a matrix determinant of order 6 or higher order ?
A2. Computing determinants
Answer 2, posted on April 9, 2019
================
On the Web page of Wikipedia given in answer 1,
see the following part of this page:
Computing determinants:
https://en.wikipedia.org/wiki/Gaussian_elimination#Computing_determinants
With best regards, Jean-Claude
A3. Use of elementary matrices
Answer 3, posted on April 10, 2019
The original question is not clear:
We cannot solve an object.
We cannot solve a number.
We cannot solve the number 2.
We cannot solve a determinant.
We can solve a problem.
We can solve an equation.
We can compute a determinant.
The following document shows that the method
of Gaussian elimination suggested by Mercedes in answer 1
can be expressed by a product of elementary matrices:
Philippe Laval
http://ksuweb.kennesaw.edu/~plaval/
Kennesaw State University
University System of Georgia, USA
https://www.kennesaw.edu/about/
Review notes
http://ksuweb.kennesaw.edu/~plaval/review.html
Math 3260, Linear Algebra
Elementary matrices
http://ksuweb.kennesaw.edu/~plaval/math3260/elemmat.pdf
1.5.4 page 44, pdf-page 6:
Gaussian Elimination and Elementary Matrices
This section shows that every square matrix with complex coefficients
can be expressed as a product of elementary matrices
and a triangular matrix.
Then we can compute the determinant of the original matrix
by using the theorem that says that
the determinant of a product of square matrices
of the same size
is equal to the product of the determinants of these matrices.
The determinant of each of the elementary matrices in the product
is very easy to compute.
To compute the determinant of the triangular matrix,
we use the theorem that says that
it is equal to the product of the entries along the main
diagonal of the triangular matrix.
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