几对对偶命题的证明  

The Proof of Several Dual Propositions

作　　者：谭福玲[1] 

机构地区：[1]黑河学院数学系,黑龙江黑河164300

出　　处：《黑河学院学报》2012年第5期125-128,共4页Journal of Heihe University

摘　　要：利用矩阵秩的知识、两点重合的概念及两线重合的概念给出两点重合的充要条件及两线重合的充要条件.根据组成点的齐次坐标的各数及组成直线的齐次线坐标的各数均不全为零,结合线性方程组解的知识,得到两个不同点连线的齐次坐标方程及该直线的线坐标、两不同直线的交点的方程及该点的坐标、三个不同点共线的充要条件及其推论以及三条不同直线共点的充要条件及其推论等。通过对对偶命题的证明,可为教师提供教学参考或为学生提供学习参考.Using the matrix rank knowledge, the two points overlapping and two line overlapping concepts are the necessary and sufficient condition of them. According to the size and composition of linear homogeneous line coordinates of each number are not zero. Combined with linear equations solution of the knowledge, two different points connection of the homogeneous coordinate equations and the straight line coordinates , two different linear nodal equations and the coordinate of the point, three different points collinear with the sufficient and necessary conditions and the inference as well as three different linear concurrent the sufficient and necessary conditions and the inferences are got. Based on dual proposition proving process, it can provide teachers with teaching reference or students with learning references.

关 键 词：点 直线 对偶命题 齐次坐标 方程 

分 类 号：O13[理学—数学]