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

Hello!

Prove:

[tex]A(\vec{a}+\vec{b}) = A\vec{a} + A\vec{b}[/tex]

Where A is a matrix and T (in the following section) is a transformation.

2. Relevant equations

[tex]T(\vec{a}) + T(\vec{b}) = T(\vec{a}+\vec{b})[/tex]

[tex]T(\vec{a}) = A\vec{a}[/tex]

[tex]T(\vec{b}) = A\vec{b}[/tex]

3. The attempt at a solution

If [tex]\vec{a}+\vec{b} = \vec{c}[/tex]

[tex]T(\vec{a}+\vec{b}) = T(\vec{c}) = Ac = A(\vec{a}+\vec{b})[/tex]

[tex]T(\vec{a}+\vec{b}) = A(\vec{a}+\vec{b}) = T(\vec{a}) + T(\vec{b}) = A\vec{a} + A\vec{b}[/tex]

Is this a sufficient proof? I can do it the more arduous way, but I think this is a proof, isn’t it?

Any help appreciated.

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# Homework Help: Matrix vector product and linear transformation proof

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