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October 12th, 2016, 04:52 PM  #1 
Newbie Joined: Oct 2016 From: New York Posts: 1 Thanks: 0  True or False Linear Algebra Theory Question
True or False?

October 30th, 2016, 04:44 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,939 Thanks: 794 
The condition that "$\displaystyle A(2\vec{v})= \vec{0}$" is peculiar and unnecessary. For A any linear transformation, [math[A(2\vec{v})= 2A(\vec{v}= \vec{0}[/math] if and only if $\displaystyle A(\vec{v})= \vec{0}$ and we were already told that there were nonzero v such that $\displaystyle A(\vec{v})= \vec{0}$. Also in order that this be true. the vector space must have dimension greater than 1 but I don't believe that is said here. 

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