(x,y)称为数对,其中x,y都是任意实数,定义数对的加法、乘法运算如下:(x1,y1)+(x2,y2)=(x1+x2,y1+y2)(x1,y1)•(x2,y2
题型:单选题难度:简单来源:不详
(x,y)称为数对,其中x,y都是任意实数,定义数对的加法、乘法运算如下: (x1,y1)+(x2,y2)=(x1+x2,y1+y2) (x1,y1)•(x2,y2)=(x1x2-y1y2,x1y2+y1x2),则( )不成立.A.乘法交换律:(x1,y1)•(x2,y2)=(x2,y2)•(x1,y1) | B.乘法结合律:(x1,y1)•(x2,y2)•(x3,y3)=(x1,y1)•[(x2,y2),(x3,y3)] | C.乘法对加法的分配律:(x,y)•[(x1,y1)+(x2,y2)]=[(x,y)•(x1,y1))+((x,y)•(x2,y2)] | D.加法对乘法的分配律:(x,y)+[(x1,y1)•(x2,y2)]=[(x,y)+(x1,y1)]•[(x,y)+(x2,y2)] |
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答案
A、由(x2,y2)•(x1,y1) =(x1x2-y1y2,x1y2+y1x2) =(x1,y1)•(x2,y2)可知,乘法交换律成立,A正确; B、由[(x1,y1)•(x2,y2)]•(x3,y3) =(x1x2-y1y2,x1y2+y1x2)•(x3,y3) =(x1x2x3-y1y2x3-x1y2y3-y1x2y3,x1x2y3-y1y2x3+x1y2x3+y1x2x3) =(x1,y1)•(x2x3-y2y3,x2y3+y2x3)=(x1,y1)•[(x2,y2)•(x3y3)]可知,乘法结合律成立,B正确; C、由(x,y)•[(x1,y1)+(x2,y2)] =(x,y)•(x1+x2,y1+y2) =[x(x1+x2)-y(y1+y2),x(y1+y2)+y(x1+x2)] =(xx1-yy1,xy1+yx1)+(xx2-yy2,xy2+yx2) =[(x,y)•(x1,y1)]+[(x,y)•(x2,y2)]可知,乘法对加法的分配律成立,C正确; D、由(1,0)+[(1,0)•(1,0)] =(1,0)+(1,0) =(2,0)≠(2,0)•(2,0) =[(1,0)+(1,0)•((1,0)+(1,0))]可知,加法对乘法的分配律不成立,D错误. 不成立的是D. 故选D. |
举一反三
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