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Appa
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Homework Statement
Suppose that the mapping F:Rn[tex]\rightarrow[/tex]Rm is continuously differentiable and that there is a fixed mxn matrix A so that
DF(x)=A for every x in Rn.
Prove that then F is a mapping such that F(x)=Ax+c for some c[tex]\in[/tex]Rm
Homework Equations
DF(x)ij= [tex]\partial[/tex]Fi(x)/[tex]\partial[/tex]xj (the ijth entry of the derivative matrix)
The Attempt at a Solution
I tried to solve this with the first-order approximation F(x)=F(xo)+F´(xo)(x-xo) +[tex]\epsilon[/tex](x-xo)||x-xo||
Where [tex]\epsilon[/tex](x-xo)||x-xo|| approaches naught.
But it didn't amount to anything sensible and I'm not sure what to do... What should I try next?