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Homework Help: Linear operator exercise i can't understand

  1. May 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Let x=(x1,x2,x3), Ax:=(x2-x3,x1,x1+x3), Bx:=(x2,2x3,x1)

    Find: (3B+2A2)x.

    2. Relevant equations

    3. The attempt at a solution

    Warning: I have no idea what I'm doing!

    (3B+2A2)x = 3Bx+2A2x

    3Bx = (3x2,6x3,3x1)

    Now to find 2A2x. Considering that an index has a higher priority than multiplication, the following is probably illegal:

    2*A*Ax = 2* A(x2-x3,x1,x1+x3) = 2 * (x1-x1-x3,x2-x3,x2-x3+x1+x3) = (-2x3,2x2-2x3,2x2+2x1)

    Now to sum up:

    (3x2,6x3,3x1) + (-2x3,2x2-2x3,2x2+2x1)...

    Suggestions? I don't even know what kind of exercise this really is, so I was unable to find anything helpful on the internet...
  2. jcsd
  3. May 19, 2012 #2
    Try and construct the matrices of A and B, you might find that more helpful

    You've done the right thing where you said [itex]2A^2x=2AAx[/itex]
    I'm not sure what you mean by 'an index has a higher priority than multiplication', an index IS multiplication. Sounds like you've not washed that FOIL/BEMDAS/OoO stuff out of your head :biggrin:
    Matrix multiplication is assosiative, you can multiply the two A's or the 2 by an A in whatever order you want.
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