Linear operator exercise i can't understand

[Deimantas]

Homework Statement

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

Find: (3B+2A²)x.

Homework Equations

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...

 

[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.