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Linear Algebra - Basis for a row space

  1. Jul 20, 2010 #1
    A =
    Code (Text):

     1  2 -1  3
     3  5  2  0
     0  1  2  1
    -1  0 -2  7
    Problem: Find a basis for the row space of A consisting of vectors that are row vector of A.

    My attempt:

    I transpose the matrix A and put it into reduced row echelon form. It turns out that there are leading ones in every column. Therefore, the basis includes every row vector from A.

    Is this the correct way to handle this problem?
  2. jcsd
  3. Jul 20, 2010 #2


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    Yes, that works.
  4. Jul 20, 2010 #3


    Staff: Mentor

    What you found means that the rows of A form a basis for R4, meaning that every vector in R4 can be written as a linear combination of the four vectors that are the rows of A.
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