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August 25th, 2015, 02:55 PM   #1
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Linear Independence and Linear Dependence.

On each item to determine whether the vectors of the vector space V are LI or LD.
b) $x-1,x^{2}+1$ and $x^{3}-x^{2}-x+3$ in $V=P_{3}(\mathbb{R})$
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August 26th, 2015, 09:22 AM   #2
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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?
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Last edited by Country Boy; August 26th, 2015 at 09:26 AM.
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