| gauss_solve {Matrix} | R Documentation |
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm
for solving systems of linear equations. It consists of a sequence of row-wise
operations performed on the corresponding matrix of coefficients. This method can
also be used to compute the rank of a matrix, the determinant of a square matrix,
and the inverse of an invertible matrix. The method is named after Carl Friedrich
Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of
elementary row operations to modify the matrix until the lower left-hand corner of
the matrix is filled with zeros, as much as possible. There are three types of
elementary row operations:
+ Swapping two rows,
+ Multiplying a row by a nonzero number,
+ Adding a multiple Of one row To another row.
Using these operations, a matrix can always be transformed into an upper triangular
matrix, And In fact one that Is In row echelon form. Once all Of the leading coefficients
(the leftmost nonzero entry In Each row) are 1, And every column containing a leading
coefficient has zeros elsewhere, the matrix Is said To be In reduced row echelon form.
This final form Is unique; In other words, it Is independent Of the sequence Of row
operations used. For example, In the following sequence Of row operations (where two
elementary operations On different rows are done at the first And third steps), the
third And fourth matrices are the ones In row echelon form, And the final matrix Is
the unique reduced row echelon form.
gauss_solve(problem,
y = NULL);a vector of the result x