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Math Help - Simple question regarding linear equation ?

  1. #1
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    Simple question regarding linear equation ?

    Find the value a for which the following system of linear equations has no solution. Solve the system when a = 1.

    x1 + 2x2 + 3x3 = 13
    -2x1 + x2 - x3 = 4
    3x1 + ax3 = -1

    I am able to do the following. Solve the system when a = 1. The answer i got is x1 = -1, x2 = 4, x3 = 2. which is correct

    But i am not sure on how to do this ? Find the value a for which the following system of linear equations has no solution.

    Any help provided will be greatly appericiated.
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  2. #2
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    Quote Originally Posted by tester85 View Post
    Find the value a for which the following system of linear equations has no solution. Solve the system when a = 1.

    x1 + 2x2 + 3x3 = 13 .... (1)
    -2x1 + x2 - x3 = 4 .... (2)
    3x1 + ax3 = -1 .... (3)

    I am able to do the following. Solve the system when a = 1. The answer i got is x1 = -1, x2 = 4, x3 = 2. which is correct

    But i am not sure on how to do this ? Find the value a for which the following system of linear equations has no solution.

    Any help provided will be greatly appericiated.
    There are many approaches.

    A simple one is to note that if you take equation (1) - 2 x equation (2) and simplify you get:

    x_1 + x_3 = 1 \Rightarrow 3 x_1 + 3 x_3 = 3.

    Clearly this will be inconsistent with equation (3) if a = 3.
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  3. #3
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    Great i get it now thanks a lot.
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