Mathematical methods for physicists(Numerical problems)

[Saad i Riaz]

Homework Statement

Show how to find A and B, given A+B and A-B ??

 

[Bill Foster]

Are they vectors?

Doesn't really matter.

$$\textbf{A}+\textbf{B}=\textbf{x}$$
$$\textbf{A}-\textbf{B}=\textbf{y}$$

Do you know how to solve a system of linear equations?

 

[Saad i Riaz]

ya these are vectors

 

[Bill Foster]

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.

 

[Saad i Riaz]

please explain me in detail becoz i have tried but my answer is not correct...

 

[Bill Foster]

$$\textbf{A}+\textbf{B}=\textbf{x}$$ (1)
$$\textbf{A}-\textbf{B}=\textbf{y}$$ (2)

Add eq (1) and (2):

$$\left(\textbf{A}+\textbf{B}=\textbf{x}\right) + \left(\textbf{A}-\textbf{B}=\textbf{y}\right)$$
$$\left(\textbf{A}+\textbf{B}+\textbf{A}-\textbf{B}\right) = \left(\textbf{x}+\textbf{y}\right)$$
$$\left(\textbf{A}+\textbf{A}\right) = \left(\textbf{x}+\textbf{y}\right)$$
$$\left(2\textbf{A}\right) = \left(\textbf{x}+\textbf{y}\right)$$
$$\textbf{A} = \frac{\textbf{x}+\textbf{y}}{2}$$

Subtract eq (2) from eq (1):

$$\left(\textbf{A}+\textbf{B}=\textbf{x}\right) - \left(\textbf{A}-\textbf{B}=\textbf{y}\right)$$
$$\textbf{B} = \frac{\textbf{x}-\textbf{y}}{2}$$

 

[Saad i Riaz]

Thnx a lot for helping me.....