Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: LINEAR ALGEBRA: 3 vecotrs in R^4 (with 6 variables) - Are they linearly independent?

  1. Oct 9, 2006 #1
    LINEAR ALGEBRA: 3 vecotrs in R^4 (with 6 variables) -- Are they linearly independent?

    For which values of the constants a, b, c, d, e, anf f are the following vectors linearly independent? Justify your answer.


    I figure that one would setup an equation:



    How does one proceed?
  2. jcsd
  3. Oct 10, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You want to find a rule for when x, y, and z are all zero. Start with zf=0. When is z not zero?

    Then you can take a look at your second equation, which should be yc + ze ;)
  4. Oct 10, 2006 #3


    User Avatar
    Homework Helper

    Do you know how to solve a system of linear equations? I suggest you try investigating the determinant of the system. Further on, what is the definition of linear independence? What must x, y, and z equal?
  5. Oct 10, 2006 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    I suggest you do not since it is not a system of 4 vectors in R^4 but 3, so there is no determinantal way to proceed, unless you wish to add a fourth arbitrary vector in that is not in the span of the first three. But that is unnecessarily complicated, although not particularyly hard. However if you can see how to do that then you can see the answer anyway. You can simply do it by inspection.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook