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Express a as a linear combination of b and c

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data

    [itex]a=\left(
    \begin{array}{c}
    -1 \\
    3 \\
    13
    \end{array}
    \right)[/itex]

    [itex]b=\left(
    \begin{array}{c}
    1 \\
    2 \\
    2
    \end{array}
    \right)[/itex]

    [itex]c=\left(
    \begin{array}{c}
    1 \\
    3 \\
    5
    \end{array}
    \right)[/itex]


    3. The attempt at a solution

    Am I supposed to determine this from inspection or through a process?
     
  2. jcsd
  3. Jun 16, 2009 #2
    a=-6b+5c from simultaneous eqautions its sorted.
     
  4. Jun 16, 2009 #3
    There is a process you can do to solve this (although some of these problems are easy enough to be solved through inspection). You want to write a as a linear combination of b and c, so write it like this:

    x[tex]\vec{b}[/tex] + y[tex]\vec{c}[/tex] = [tex]\vec{a}[/tex]

    Then you solve for x and y. This can be done easily by creating a matrix and putting it in RREF.

    Your matrix should look like this:

    1 1 : -1
    2 3 : 3
    2 5 : 13

    So use Gaussian elimination, put it in RREF and you will have your answers for x and y. (Sorry about the sad looking matrix but I suck with latex lol)
     
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