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Math Help - Solving for 2 systems at once

  1. #1
    DrZ
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    Solving for 2 systems at once

    I dont think I understand what this question is asking, if someone could explain what it means with its explanation it would help a lot.

    solve the 2 systems

    x1 + 2x2 - 2x3 =1 x1 + 2x2 - 2x3 = 9
    2x1 + 5x2 +x3 = 9 2x1 + 5x2 +x3 = 9
    x1 + 3x2 + 4x3 = 9 x1 + 3x2 + 4x3 = -2

    the question gives this explanation

    by doing elimination on a 3x5 augmented matrix and the performing two back substitutions.


    I thought it meant to put the two systems together, but since the 2nd row of equations are the same there would only be 5, not 6 I would use so it would be 3x5.

    1 2 -2 1
    2 5 1 9
    1 3 4 9
    1 2 -2 9
    1 3 4 -2

    but then that would make 2 rows
    0 0 0 x
    and then wouldn't it be inconsistent. But the book has answers to the question so its not that. What is this question even asking me to do?
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  2. #2
    A Plied Mathematician
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    It's asking you to solve two systems that happen to have the same coefficient matrices, but different RHS's. So take the augmented matrix suggested, namely,

    \left[<br />
\begin{array}{rrr|rr}<br />
1 &2 &-2 &1 &9\\<br />
2 &5 &1 &9 &9\\<br />
1 &3 &4 &9 &-2<br />
\end{array}<br />
\right],

    and perform ero's on it in order to make it upper triangular. (Usual Gaussian elimination.) What do you get?
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  3. #3
    DrZ
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    thanks. weird the textbook does not show any matrices with the 2 right columns at all in the first section where the question came from.

    I ended up getting it triangular and getting the right answers for each system.
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  4. #4
    A Plied Mathematician
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    Quote Originally Posted by DrZ View Post
    thanks. weird the textbook does not show any matrices with the 2 right columns at all in the first section where the question came from.

    I ended up getting it triangular and getting the right answers for each system.
    Excellent!
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