搜搜做题作业网请帮忙解这个数分的题Find an analytic (symbolic) description of the map
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请帮忙解这个数分的题
Find an analytic (symbolic) description of the mapping that assigns to a non-zero vector x∈ Rn the vector of length 2 that points in the direction opposite to x.In case n = 3 ,that is if x = (x,y,z) ,determine the component functions of this mapping.Is it possible to define the image of the mapping at (0,0,0) such that it is continuous on R3 Justify your
answer.
Find an analytic (symbolic) description of the mapping that assigns to a non-zero vector x∈ Rn the vector of length 2 that points in the direction opposite to x.In case n = 3 ,that is if x = (x,y,z) ,determine the component functions of this mapping.Is it possible to define the image of the mapping at (0,0,0) such that it is continuous on R3 Justify your
answer.
题目的意思是找一个向量映射使得|f(x)|=2,且方向与x相反
以n=3为例
a=(x,y,z)≠0,|a|=(x^2+y^2+z^2)^(1/2)
f(a)=(-2x/[3^(1/2)|a|],-2y/[3^(1/2)|a|],-2z/[3^(1/2)|a|])
要让f在(0,0,0)连续,只需定义f((0,0,0))=(0,0,0)即可
验证很简单
以n=3为例
a=(x,y,z)≠0,|a|=(x^2+y^2+z^2)^(1/2)
f(a)=(-2x/[3^(1/2)|a|],-2y/[3^(1/2)|a|],-2z/[3^(1/2)|a|])
要让f在(0,0,0)连续,只需定义f((0,0,0))=(0,0,0)即可
验证很简单
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