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suneja

  • 3 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?

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  1. nitz
    • 3 years ago
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    since Sx is a invertible matrix....so it has non -zero

  2. nitz
    • 3 years ago
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    elements

  3. suneja
    • 3 years ago
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    ya the ans to it is R^3 to R^2

  4. nitz
    • 3 years ago
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    i mean it has to be a non zero matrix

  5. nitz
    • 3 years ago
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    doesnt matter if one of the elements is zero

  6. suneja
    • 3 years ago
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    now how did they gt R^3 in case of matrices it cud hav been R^2 as well

  7. suneja
    • 3 years ago
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    ya its non zero

  8. nitz
    • 3 years ago
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    ya...if the matrix is 2*2 ...it should be R^2

  9. suneja
    • 3 years ago
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    dats ma point

  10. nitz
    • 3 years ago
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    Let me see.....

  11. suneja
    • 3 years ago
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    @nitz in case u cud also find the Jacobian for tis equation

  12. suneja
    • 3 years ago
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    its S... can u explain??

  13. nitz
    • 3 years ago
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    ya

  14. nitz
    • 3 years ago
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    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
    • 3 years ago
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    in case of a variable of single function it might be:: partial derivative of (F(x,c)) wrt to x =S

  16. suneja
    • 3 years ago
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    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
    • 3 years ago
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    gt dat n wat abt the domain and range cud u figure dat out

  18. nitz
    • 3 years ago
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    sorry i was to write their function of two variables...

  19. suneja
    • 3 years ago
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    ya cz partial is used for more than one variables

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