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- anonymous

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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- anonymous

- jamiebookeater

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- anonymous

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

- anonymous

elements

- anonymous

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

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- anonymous

i mean it has to be a non zero matrix

- anonymous

doesnt matter if one of the elements is zero

- anonymous

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

- anonymous

ya its non zero

- anonymous

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

- anonymous

dats ma point

- anonymous

Let me see.....

- anonymous

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

- anonymous

its S... can u explain??

- anonymous

ya

- anonymous

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 ))

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

ya cz partial is used for more than one variables

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