Question

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?

Answer 1

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

Answer 2

elements

Answer 3

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

Answer 4

i mean it has to be a non zero matrix

Answer 5

doesnt matter if one of the elements is zero

Answer 6

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

Answer 7

ya its non zero

Answer 8

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

Answer 9

dats ma point

Answer 10

Let me see.....

Answer 11

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

Answer 12

its S... can u explain??

Answer 13

ya

Answer 14

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 ))

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

ya cz partial is used for more than one variables