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 August 24th, 2015, 08:28 AM #1 Member   Joined: Mar 2015 From: Brasil Posts: 90 Thanks: 4 Linear Independence and Linear Dependence. Prove that the three vectors are $\mathbb{R}^{2}$ LD (Linear Dependence). Generalize this result to $\mathbb{R}^{n}$. Last edited by skipjack; August 24th, 2015 at 11:25 AM.
 August 24th, 2015, 10:45 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,403 Thanks: 2477 Math Focus: Mainly analysis and algebra Suppose we are given vectors $\vec u$, $\vec v$ and $\vec w$ all in $\mathbb R^2$. If $\vec u$ and $\vec v$ are LD then there exist non-zero real numbers $a$ and $b$ such that $a\vec u + b\vec v = 0$. And we can easily expand this linear combination to include $\vec w$ too. If $\vec u$ and $\vec v$ are LI, they must span $\mathbb R^2$ (do you need to prove this?) and so $\vec w = a\vec u + b\vec v$ for some real numbers $a$ and $b$. Thanks from Luiz

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