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August 25th, 2015, 02:55 PM  #1 
Member Joined: Mar 2015 From: Brasil Posts: 90 Thanks: 4  Linear Independence and Linear Dependence.
On each item to determine whether the vectors of the vector space V are LI or LD. b) $x1,x^{2}+1$ and $x^{3}x^{2}x+3$ in $V=P_{3}(\mathbb{R})$ 
August 26th, 2015, 09:22 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,168 Thanks: 867 
Once again you have asked a question without letting us know what you do understand about this. To determine whether or not a set of vectors is "linear independent" or "linear dependent", see whether or not the set satisfies the definition of "linearly independent". Do you know what that definition is? $\displaystyle a(x 1)+ b(x^2+ 1)+ c(x^3 x^2 x+ 3)= 0$ for all x if a= b= c= 0. Is it 0, for all x, for any other values of a, b, and c? To answer that, expand each term so you have $\displaystyle ( )x^3+ ( )x^2+ ( )x+ ( )= 0$ and each ( ) must be equal to 0. That gives you three equations to solve for a, b, and c. Is a= b= c= 0 the only solution? Last edited by Country Boy; August 26th, 2015 at 09:26 AM. 

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