1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Combination Method

  1. Jan 4, 2008 #1

    Mtl

    User Avatar

    [SOLVED] Linear Combination Method

    1. The problem statement, all variables and given/known data
    Show, using the linear combination method, that the vectors below are non-coplanar or independent. Be complete
    d= [2,-1,-2], e=[1,1,1] , and f = [1,-5,8]

    2. Relevant equations
    Ok so I'm assuming, I am supposed to use Cramer's Rule here. But the problem is I don't fully understand it.

    3. The attempt at a solution
     
  2. jcsd
  3. Jan 4, 2008 #2

    Shooting Star

    User Avatar
    Homework Helper

    Just find the magnitude of the determinant.
     
  4. Jan 5, 2008 #3

    Defennder

    User Avatar
    Homework Helper

    Why do you have to use Cramer's rule? There are many ways to do the question. One way, as Shooting star has pointed out, but not fully enough is to treat the three vectors as row vectors in a 3x3 matrix. Now what do you remember of the properties of a matrix whose row vectors are linearly independent?
     
  5. Jan 5, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What, exactly do you mean by "the linear combination method"? I would think that it just means to use the definition of "independent"- that the only way a linear combination of the vectors can be 0 is if the coefficients are all 0: Show that
    [itex]\alpha [2, 1, -2]+ \beta [1, 1, 1]+ \gamma [1, -5, 8]= [0, 0, 0][/itex] only if [itex]\alpha= \beta= \gamma= 0[/itex].
     
  6. Jan 5, 2008 #5

    Shooting Star

    User Avatar
    Homework Helper

    Why not take the shortcut and arrange the three vectors as three rows and show that the det not equal to 0? He will be finding the det anyway to solve the eqns, if he uses Kramer's rule.
     
  7. Jan 5, 2008 #6

    Mtl

    User Avatar

    OK, thanks for your input, I think I have it now.
     
  8. Jan 6, 2008 #7

    Mtl

    User Avatar

    New Question... Given that the two vectors u=(2a+b) and v=(4a-3b) are perpendicular and that |a|=3 and |b|=6, then find the angle between a and b.

    So I pretty sure i need to set the dot product of u and v = to zero. Then there is probably some sort of way to rearange it, of which I am not sure.
     
  9. Jan 6, 2008 #8

    Shooting Star

    User Avatar
    Homework Helper

    Just take the scalar product of u and v, which is zero. You'll get terms containing a^2, b^2 and a.b. So, find cos theta.
     
  10. Jan 6, 2008 #9

    Mtl

    User Avatar

    Thanks for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear Combination Method
  1. Linear Combinations (Replies: 7)

  2. Linear combination (Replies: 16)

  3. Linear Combinations (Replies: 3)

  4. Linear combinations? (Replies: 1)

  5. Linear combination (Replies: 2)

Loading...