# Linear operator exercise i can't understand

1. May 19, 2012

### Deimantas

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. May 19, 2012

### genericusrnme

Try and construct the matrices of A and B, you might find that more helpful

You've done the right thing where you said $2A^2x=2AAx$
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
Matrix multiplication is assosiative, you can multiply the two A's or the 2 by an A in whatever order you want.