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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: 7,614 Thanks: 2603 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 Tags dependence, independence, linear Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Luiz Linear Algebra 1 August 19th, 2015 09:09 AM autumn94 Linear Algebra 1 March 29th, 2015 02:14 PM phongchaychua Linear Algebra 2 April 27th, 2014 05:08 AM Spennet Linear Algebra 2 August 18th, 2011 08:00 AM Singularity Linear Algebra 1 February 4th, 2010 05:32 PM

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