Definition and calculation of n-order determinant

According to certain rules, the algebraic sum formed by the product of a group of (n) numbers (called elements) arranged in a square is called the determinant of order n.

For example, the second-order lines of four numbers A, B, C and D are written as

Its expansion was in AD-BC.

Nine numbers a 1, a2, a3; b 1，b2，B3； The third determinant of c 1, c2, c3 is written as

The expansion formula is a1b2c3+a2b3c1+a3b1C2-a1b3c2-a2b1C3-a3b2c1. Determinant originated from the solution of linear equations and is widely used in all branches of mathematics. In algebra, determinant can be used to simplify some expressions, such as solving linear equations with fewer unknowns.

1683, Guan Xiaohe of Japan first put forward the concept of determinant and its expansion method. Leibniz also announced his discovery of determinant in a letter in 1693 (unpublished before his death).