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对同一个量,用两种,甚至更多种不同的方法计算,得到的结果不管形式如何,实质是完全一样的。由此,导出一些等式,也可以建立不等式或其他关系。这种方法称为算两次原理或 Fubing原理。在反证法中,算两次又常常用来导出矛盾。例1 如图是由16个数组成一个4×4的数阵,其中每一个数都为±1,每行右边的数是这行四个数的积,每列下边的数是该列四个数的积.这八个积的和为零.问:能否作出一个由±1组成的,25×25的数阵,使每行的积
For the same quantity, two or more different methods are used to calculate the result. The result is exactly the same regardless of the form. From this, some equations can be derived and inequalities or other relationships can also be established. This method is called two principles or Fubing principle. In counter-evidence, counting twice is often used to derive contradictions. Example 1 As shown in the figure, a number of 4×4 arrays are composed of 16 numbers, each of which is ±1. The number on the right of each row is the product of four rows of this row. The number of the bottom row of each row is the number of columns. The product of the number. The sum of these eight products is zero. Q: Can you make a 25×25 matrix consisting of ±1, so that the product of each row