(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let x=(x_{1},x_{2},x_{3}),Ax:=(x_{2}-x_{3},x_{1},x_{1}+x_{3}),Bx:=(x_{2},2x_{3},x_{1})

Find: (3B+2A^{2})x.

2. Relevant equations

3. The attempt at a solution

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

(3B+2A^{2})x = 3Bx+2A^{2}x

3Bx = (3x_{2},6x_{3},3x_{1})

Now to find 2A^{2}x. Considering that an index has a higher priority than multiplication, the following is probably illegal:

2*A*Ax = 2* A(x_{2}-x_{3},x_{1},x_{1}+x_{3}) = 2 * (x_{1}-x_{1}-x_{3},x_{2}-x_{3},x_{2}-x_{3}+x_{1}+x_{3}) = (-2x_{3},2x_{2}-2x_{3},2x_{2}+2x_{1})

Now to sum up:

(3x_{2},6x_{3},3x_{1}) + (-2x_{3},2x_{2}-2x_{3},2x_{2}+2x_{1})...

Suggestions? I don't even know what kind of exercise this really is, so I was unable to find anything helpful on the internet...

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# Homework Help: Linear operator exercise i can't understand

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