计算n阶行列式的若干方法举例（Examples of some methods for calculating order n determinant）.docVIP

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计算n阶行列式的若干方法举例（Examples of some methods for calculating order n determinant）.doc

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计算n阶行列式的若干方法举例（Examples of some methods for calculating order n determinant）

计算n阶行列式的若干方法举例（Examples of some methods for calculating order n determinant） Examples of some methods for calculating order n determinant LAN min Abstract: linear algebra is a required basic mathematics course for students of science and engineering universities. The calculation of determinant is a difficult and important point in linear algebra, especially the calculation of the determinant of order n. In the course of studying, students generally have many difficulties and difficult to master. There are many ways to calculate the n order determinant, but to a specific problem, we should choose the appropriate method according to its characteristics. Keywords: n order determinant method A lot of calculation method of N determinant, unless the zero elements can be used to calculate (less defined in a column or a row START II full expansion), more is the use of the properties of the determinant calculation, with particular attention to observe the characteristics for the problem, the method is flexible, it is worth noting. One determinant, sometimes a different method. Here are some commonly used methods, and examples. 1. direct calculation using determinant definitions Example 1 calculates the determinant EMBED Equation.DSMT4 The item that is not zero in Dn is expressed as a general form EMBED Equation.DSMT4 The inverse number T column arrangement (n - 1 N - 2... 1n) equal to EMBED Equation.DSMT4, so EMBED Equation.DSMT4 2. use the nature of determinant Example 2 a n order determinant satisfies the elements of EMBED Equation.DSMT4 EMBED Equation.DSMT4 We call Dn the antisymmetric determinant, and prove that the odd order antisymmetric determinant is zero Proof: EMBED Equation.DSMT4 knows EMBED Equation.DSMT4, i.e. EMBED Equation.DSMT4 So the determinant Dn can be represented as EMBED Equation.DSMT4 The nature of the determinant EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 When n is odd, Dn = = Dn is obtained, hence Dn = 0. 3. i