1. The problem statement, all variables and given/known data 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 2. Relevant equations DF(x)ij= [tex]\partial[/tex]Fi(x)/[tex]\partial[/tex]xj (the ijth entry of the derivative matrix) 3. 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?