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In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...
Download as PDF; Printable version; ... The Leibniz formula for the determinant of a 3 × 3 matrix is the ... without proof, Cramer's rule. [27] Both Cramer and also ...
Download as PDF; Printable version ... Cramer's rule is an explicit formula for the solution of a system of linear ... large determinants are most easily computed ...
In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule).
Download as PDF; Printable version; In other projects ... Cayley–Menger determinant; Circulant matrix; Cramer's rule; ... Jacobi's formula; Jacobian matrix and ...
This expansion can be used for a recursive definition of determinants (taking as starting case the determinant of a 1-by-1 matrix, which is its unique entry, or even the determinant of a 0-by-0 matrix, which is 1), that can be seen to be equivalent to the Leibniz formula. Determinants can be used to solve linear systems using Cramer's rule ...
By Cramer's rule, the solution is a rational number in which the denominator is the determinant of this submatrix. This determinant must by +1 or −1; therefore the solution is an integer vector. Therefore all corner coordinates are integers.
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...