December 9th, 2016, 11:57 AM  #1 
Newbie Joined: Dec 2016 From: Natal  Brazil Posts: 10 Thanks: 0  Linear independence
For what real values of x do the vectors v1 = (1, 2, x), v2 = (1, 1, 1) and v3 = (x, 6, 2) form a linearly dependent set?

December 9th, 2016, 02:34 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,437 Thanks: 528 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle \lambda _1 v_1 + \lambda _2 v_2 + \lambda _3 v_3 = 0$ where at least one of the $\displaystyle \lambda _i \neq 0$. The other, more efficient way, is to use matrices: $\displaystyle \left ( \begin{matrix} 1 & 1 & x \\ 2 & 1 & 6 \\ x & 1 & 2 \end{matrix} \right ) \cdot \left ( \begin{matrix} \lambda _1 \\ \lambda _2 \\ \lambda _3 \end{matrix} \right ) = \left ( \begin{matrix} 0\\ 0 \\ 0 \end{matrix} \right )$ If the determinant of the coefficient matrix is not 0 then the system is linearly independent. Dan  
December 9th, 2016, 08:29 PM  #3 
Newbie Joined: Dec 2016 From: Natal  Brazil Posts: 10 Thanks: 0 
Thank you so much !!!

December 10th, 2016, 06:52 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,211 Thanks: 555 
Notice that topsquark said "If the determinant of the coefficient matrix is not 0 then the system is linearly independent." You want linearly dependent.


Tags 
dependence, independence, linear 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Linear Independence and Linear Dependence.  Luiz  Linear Algebra  7  August 29th, 2015 12:54 PM 
Linear Independence and Linear Dependence.  Luiz  Linear Algebra  1  August 26th, 2015 09:22 AM 
Linear Independence and Linear Dependence.  Luiz  Linear Algebra  5  August 24th, 2015 02:10 PM 
Linear Independence and Linear Dependence.  Luiz  Linear Algebra  1  August 24th, 2015 10:45 AM 
Linear independence & linear dependence  autumn94  Linear Algebra  1  March 29th, 2015 02:14 PM 