My Math Forum Linear Independence and Linear Dependence.

 Linear Algebra Linear Algebra Math Forum

 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) $x-1,x^{2}+1$ 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? Thanks from Luiz Last edited by Country Boy; August 26th, 2015 at 09:26 AM.

 Tags dependence, independence, linear

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Luiz Linear Algebra 5 August 24th, 2015 02:10 PM Luiz Linear Algebra 1 August 24th, 2015 10:45 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

 Contact - Home - Forums - Cryptocurrency Forum - Top