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Math Help - MATLAB linearly dependant vectors

  1. #1
    Junior Member
    Joined
    Apr 2008
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    MATLAB linearly dependant vectors

    hi

    Basically I'm new to Matlab and i need to show that the 4 column vectors:

    p=[4;3;-1;2;1], q=[-4;7;-9;0;3], r=[2;3;-2;0;1], s=[0;2;-2;3;1]

    ( ; means that the next number is on a new line..column vector...)

    I need to show these are linearly dependant by solving the vector equation:

    c1*p+c2*q+c3*r+c4*s=0

    Does anyone know the shortest way to solve this using Matlab?
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  2. #2
    Senior Member Peritus's Avatar
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    Nov 2007
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    c1*p+c2*q+c3*r+c4*s=0

    notice that we can write this in the following form:

    <br />
\left[ {\begin{array}{*{20}c}<br />
   p & | & q & | & r & | & s  \\<br /> <br />
 \end{array} } \right]\left[ {\begin{array}{*{20}c}<br />
   {c_1 }  \\<br />
   {c_2 }  \\<br />
   {c_3 }  \\<br />
   {c_4 }  \\<br /> <br />
 \end{array} } \right] = 0<br />


    ----------------------------------------

    \left[ {\begin{array}{*{20}c}<br />
   p & | & q & | & r & | & s  \\<br /> <br />
 \end{array} } \right] is a 5x4 matrix who's columns are the vectors p,q,r and s.

    so we've basically got a system of homogeneous equations of the following form:

    <br />
\underline{\underline A}  \cdot \underline c  = \underline 0 <br />

    so showing that the vectors are linearly dependent is equivalent to showing that A does not have a full rank, which can be tested using the fucntion rank: rank(A) < 4
    Last edited by Peritus; April 3rd 2008 at 04:09 PM.
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