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Math Help - Linear Algebra question

  1. #1
    Newbie
    Joined
    Apr 2005
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    12

    Linear Algebra question

    Hi I have this urgent linear algebra question.

    I'm given this here formula A x = b

    where A = \left[ \begin{array}{ccc} 1 & 0 & 2 \\ 2 & 1 & 3  \end{array} \right] and \left[ \begin{array}{c} b_1 \\ b_2  \end{array} \right] is a vector in R^2.

    Then I'm tasked with determing the complete set of solution for T(x) = b.

    Do do this I know that I need to solve the following matrix \left[ \begin{array}{cccc} 1 & 0 & 2 & b_1 \\ 2 & 1 & 3 & b_2  \end{array} \right] which can be row-reduced to  \left[ \begin{array}{cccc} 1 & 0 & 2 & {b_1} \\ 2 & 1 & 3 & b_2 - 2b_1  \end{array} \right]

    How do I form the set of solution for the equation T(x) = b from the row-reducet matrix???

    Secondly how do I draw this geometricly ??

    Sincerely and Best Regards,

    Fred
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  2. #2
    Newbie
    Joined
    Jun 2005
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    Orlando
    Posts
    10
    It looks like you wanted to perform the operation where you replace the second row by itself minus twice the first row, but you have to do it for each element. It's an operation on the entire row, because what you are really doing is moving around entire equations with each row op. So your last line should be


    \left[ \begin{array}{cccc} 1 & 0 & 2 & b_1 \\ 0 & 1 & -1 & b_2-2*b_1 \end{array} \right]\,
    Last edited by MathMan; June 24th 2005 at 07:40 AM.
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