- #1
nobahar
- 497
- 2
Homework Statement
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.
Homework 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]
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.