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Lin Alg - Find the basis and dimension

  1. Jul 19, 2010 #1
    Find the basis and dimension of the following homogeneous system:
    Code (Text):

    A =     |1 0 2| |x1|
            |2 1 3| |x2| = [0,0,0]
            |3 1 2| |x3|

    My attempt:

    Solving the coefficient matrix for RREF, I get the identify matrix.
    So, x1=x2=x3=0 and the only solution is a trivial one.

    Does that mean there is no basis(empty basis), or that the basis only contains the zero vector and has dimension zero?
  2. jcsd
  3. Jul 19, 2010 #2


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    The dimension is equal to the number of vectors in a basis, so if the solution space is zero-dimensional, the basis is empty.
  4. Jul 19, 2010 #3

    Thanks for the help!
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