Linear maps \(F(X)=A X\), where \(A\) is a matrix, have the property that \(F(0)=A 0=0\), so they necessarily leave the origin fixed. It is simple to extend this to include a translation,
where \(V\) is a vector. Note that \(F(0)=V\).
Find the vector \(V\) and the matrix \(A\) that describe each of the following mappings [here the light blue \(F\) is mapped to the dark red \(F]\).