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Mathematical methods for physicists(Numerical problems)

  1. Oct 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Show how to find A and B, given A+B and A-B ??
     
  2. jcsd
  3. Oct 23, 2009 #2
    Are they vectors?

    Doesn't really matter.

    [tex]\textbf{A}+\textbf{B}=\textbf{x}[/tex]
    [tex]\textbf{A}-\textbf{B}=\textbf{y}[/tex]

    Do you know how to solve a system of linear equations?
     
  4. Oct 23, 2009 #3
    ya these are vectors
     
  5. Oct 23, 2009 #4
    Using the two equations above, write A in terms of x and y, and write B in terms of x and y. You can do this by adding one equation to the other, and subtracting one equation from the other.
     
  6. Oct 24, 2009 #5
    plz explain me in detail becoz i have tried but my answer is not correct........
     
  7. Oct 24, 2009 #6
    [tex]\textbf{A}+\textbf{B}=\textbf{x}[/tex] (1)
    [tex]\textbf{A}-\textbf{B}=\textbf{y}[/tex] (2)

    Add eq (1) and (2):

    [tex]\left(\textbf{A}+\textbf{B}=\textbf{x}\right) + \left(\textbf{A}-\textbf{B}=\textbf{y}\right)[/tex]
    [tex]\left(\textbf{A}+\textbf{B}+\textbf{A}-\textbf{B}\right) = \left(\textbf{x}+\textbf{y}\right)[/tex]
    [tex]\left(\textbf{A}+\textbf{A}\right) = \left(\textbf{x}+\textbf{y}\right)[/tex]
    [tex]\left(2\textbf{A}\right) = \left(\textbf{x}+\textbf{y}\right)[/tex]
    [tex]\textbf{A} = \frac{\textbf{x}+\textbf{y}}{2}[/tex]

    Subtract eq (2) from eq (1):

    [tex]\left(\textbf{A}+\textbf{B}=\textbf{x}\right) - \left(\textbf{A}-\textbf{B}=\textbf{y}\right)[/tex]
    [tex]\textbf{B} = \frac{\textbf{x}-\textbf{y}}{2}[/tex]
     
  8. Oct 24, 2009 #7
    Thnx alot for helping me..............
     
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