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suneja
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?
since Sx is a invertible matrix....so it has non -zero
ya the ans to it is R^3 to R^2
i mean it has to be a non zero matrix
doesnt matter if one of the elements is zero
now how did they gt R^3 in case of matrices it cud hav been R^2 as well
ya...if the matrix is 2*2 ...it should be R^2
@nitz in case u cud also find the Jacobian for tis equation
its S... can u explain??
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 ))
in case of a variable of single function it might be:: partial derivative of (F(x,c)) wrt to x =S
then partial derivative of F(x,c)= Sx + G(c)=0 w.r.t x is S is dat hw v go abt it
gt dat n wat abt the domain and range cud u figure dat out
sorry i was to write their function of two variables...
ya cz partial is used for more than one variables