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Homework Help: Graduate Engineering - Linear Algebra (Graham Schmidt + more)

  1. Oct 12, 2012 #1
    1. The problem statement, all variables and given/known data
    No idea how to solve this using graham schmidt. I know how to do graham schmidt and how to solve this problem if I didn't have to use graham schmidt, but I have no idea where to start in order to get my vectors to add to V

    Found c to be 87 by using vector addition/subtraction and making it linearly dependent on other two.
    However, not sure how to find two vectors that are in span and perpendicular that add up to V just like in #1

    For b., as long as A is invertable, wouldn't it be all of the b vectors?

    2. Relevant equations
    Graham Schmidt...

    3. The attempt at a solution
    Posted above
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 12, 2012 #2


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    Well, if the question was not asking you to use the procedure, you could easily solve the augmented system and exhibit a solution.

    The point of the gram process though, is to take a set of linearly independent vectors say S, in your space and to form a orthogonal set of vectors T by using the process. The span of the new set of vectors will be equivalent to the span of your original set.

    That is, span{T} = span{S}.

    You could go even further and form an orthonormal set out of the vectors of T, but it's not required here. Finding the set T should be sufficient.
  4. Oct 12, 2012 #3
    Should I use my first two vectors in my set to find the first orthogonal vectors and the third as {1 2 3} to find the vector V2 perpindicular to my span? From there {1 2 3} minus the V2 vector to get my V1

    I'm just confused as to how I use V1 is in span, V2 is perp to span and V1+V2 = {1 2 3}
  5. Oct 12, 2012 #4
    Out of curiousity (I'm learning gram schmidt for the first time in my LA class), what application does this have to engineering? (Thinking of going into engineering)
  6. Oct 12, 2012 #5


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    Yeah, that'll work if you're planning to do what I think you're saying.
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