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Math Help - Matrix Row Operations

  1. #1
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    Matrix Row Operations

    Could someone help me with this problem? Thanks!

    6x+7y=13
    x-y=0
    x+y=12
    (Answer: x=1, y=1)

    Solve using matrix operations to get the coefficient matrix into reduced form. Write down the answer.
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  2. #2
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    Quote Originally Posted by mhitch03 View Post
    Could someone help me with this problem? Thanks!

    6x+7y=13
    x-y=0
    x+y=12
    (Answer: x=1, y=1)

    Solve using matrix operations to get the coefficient matrix into reduced form. Write down the answer.

    The system is clearly incongruent (i.e., it has no solution) since by x-y=0\,\Longrightarrow\,x=y, but this doesn't solve 6x+7y=13\,\,\,and\,\,\,also\,\,\,x+y=12.

    It's trivial to check that x=y=1 doesn't solve neither the first nor the third equation.

    Tonio
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  3. #3
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    I'm sorry, that is a typo... the last equation is x+y=2
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  4. #4
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    Quote Originally Posted by mhitch03 View Post
    I'm sorry, that is a typo... the last equation is x+y=2

    Then you only need the second and third equation to get the solution at once, and using matrices:

    \left(\begin{array}{rrr}6&7&13\\1&-1&0\\1&1&2\end{array}\right) \rightarrow\left(\begin{array}{rrr}1&-1&0\\1&1&2\\6&7&13\end{array}\right) \left(\begin{array}{rrr}1&-1&0\\0&2&2\\0&13&13\end{array}\right)\rightarrow\l  eft(\begin{array}{rrr}1&-1&0\\0&1&1\\0&0&0\end{array}\right)

    From the second row, y=1 , and from the first one x-1=0\rightarrow x=1

    Tonio
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