My Math Forum True or False Linear Algebra Theory Question

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October 12th, 2016, 04:52 PM   #1
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True or False Linear Algebra Theory Question

True or False?
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 October 30th, 2016, 04:44 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,875 Thanks: 766 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 non-zero 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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