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?
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since Sx is a invertible matrix....so it has non -zero
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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 its non zero
ya...if the matrix is 2*2 ...it should be R^2
dats ma point
Let me see.....
@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 ::
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
n wat abt the domain and range cud u figure dat out
sorry i was to write their function of two variables...