3. The vector field F(x,y)-(-y,x)" at the point (2,1) can be decomposed by Taylor expansion in the form r-2 -1 T-2 F(x,y) = Fo + S + A y - 1J + error where Fo is a constant vector, S is a constant symmetric matrix, A is a constant anti symmetric matrix, and "erro" means a vector function (x, y) satisfying G)0. Find Fo, S and A. Is there any local stretching at (2,1)? lim ()2+y Is there any local rotation? 4. Repeat the previous problem for F(x,y) = (x-y, x + y) 5. Repeat the previous problem for F(x,y)- 2 2 3. The vector field F(x,y)-(-y,x)" at the point (2,1) can be decomposed by Taylor expansion in the form r-2 -1 T-2 F(x,y) = Fo + S + A y - 1J + error where Fo is a constant vector, S is a constant symmetric matrix, A is a constant anti symmetric matrix, and "erro" means a vector function (x, y) satisfying G)0. Find Fo, S and A. Is there any local stretching at (2,1)? lim ()2+y Is there any local rotation? 4. Repeat the previous problem for F(x,y) = (x-y, x + y) 5. Repeat the previous problem for F(x,y)- 2 2