## suneja 2 years ago consider the sys of equations F(x,c)= Sx + G(c)=0 where S is an invertible 2*2 matrix and G is continuously differentiable fn and c is any real no. The domain and range of this function is?

1. nitz

since Sx is a invertible matrix....so it has non -zero

2. nitz

elements

3. suneja

ya the ans to it is R^3 to R^2

4. nitz

i mean it has to be a non zero matrix

5. nitz

doesnt matter if one of the elements is zero

6. suneja

now how did they gt R^3 in case of matrices it cud hav been R^2 as well

7. suneja

ya its non zero

8. nitz

ya...if the matrix is 2*2 ...it should be R^2

9. suneja

dats ma point

10. nitz

Let me see.....

11. suneja

@nitz in case u cud also find the Jacobian for tis equation

12. suneja

its S... can u explain??

13. nitz

ya

14. nitz

actually jacobian is generally used to make tranformations :: like u=u(x,y) v=v(x,y) then in this case jacobian of transformation is :: J=(PARTIAL DERIVATIVE OF a function of (x,y))/(PARTIAL DERIVATIVE OF a function of(u,v)) =mod((partial derivative of x wrt to u) (partial derivative of y wrt to u) (partial derivative of x wrt to v) (partial derivative of y wrt to v ))

15. nitz

in case of a variable of single function it might be:: partial derivative of (F(x,c)) wrt to x =S

16. suneja

then partial derivative of F(x,c)= Sx + G(c)=0 w.r.t x is S is dat hw v go abt it

17. suneja

gt dat n wat abt the domain and range cud u figure dat out

18. nitz

sorry i was to write their function of two variables...

19. suneja

ya cz partial is used for more than one variables