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Math Help - System of equations

  1. #1
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    System of equations

    This question is under the Matrices topic.
    I tried solving using Row Reduction and found that if a=-2, the equations are undefined.

    Actually I don't know what the question is asking about
    Attached Thumbnails Attached Thumbnails System of equations-matrices.jpg  
    Last edited by stpmmaths; November 7th 2010 at 12:56 AM.
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  2. #2
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    Quote Originally Posted by stpmmaths View Post
    This question is under the Matrices topic.
    I tried solving using Row Reduction and found that if a=-2, the equations are undefined.

    Actually I don't know what the question is asking about
    After a few row operations on the augmented matrix you get:

     <br />
\left[ <br />
\begin{array}{ccc|c} <br />
a&1&1&1\\ <br />
0&a-1&1-a&a(1-a)\\ <br />
1-a&0&a-1&(a-1)(a+1) <br />
\end{array} <br />
\right] <br />

    I suggest you now consider the cases a = 1 (which corresponds to infinite solutions) and a \neq 1. The case a \neq 1 might break down into two more cases, if there's another important value of a to consider ....
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    Discuss and find(where possible) the solutions to this system as a takes on all real values.
    What does that means?
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  4. #4
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    Quote Originally Posted by stpmmaths View Post
    What does that means?
    If you honestly have no idea, then I'm not sure why you are attempting this question. You need to think about what it means. Go back to your class notes or textbook and review similar examples.
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    The thing is that there is no example relating to this question. I was given this question and was asked to complete it

    Btw, thanks for your concern
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    Quote Originally Posted by stpmmaths View Post
    The thing is that there is no example relating to this question. I was given this question and was asked to complete it

    Btw, thanks for your concern
    If you know nothing about the theory behind this type of question then I don't see how you can be guided towards a solution. And I'm not willing to give a complete solution (particularly since it appears you would not even understand it).

    Do you know how to solve systems of linear equations using Gaussian elimination? Do you understand the three types of solutions that are possible (unique, infinite, none)? These are the things you will have to review in your class notes and textbook if you are to understand how to do this question.
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    Quote Originally Posted by mr fantastic View Post
    If you know nothing about the theory behind this type of question then I don't see how you can be guided towards a solution. And I'm not willing to give a complete solution (particularly since it appears you would not even understand it).

    Do you know how to solve systems of linear equations using Gaussian elimination? Do you understand the three types of solutions that are possible (unique, infinite, none)? These are the things you will have to review in your class notes and textbook if you are to understand how to do this question.
    I don't want the answer to this question, just want to know what is this question want us to do? Er...I think slowly getting it...

    By the way, I do know about Gaussian Elimination, the three types of solutions(infinite- 0=0, unique-number of equations=unknowns and none-Inconsistent).

    Besides, I do know Gauss-Jordan method, Augmented matrix, Eigenvalues and Eigenvectors.
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  8. #8
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    Quote Originally Posted by mr fantastic View Post
    After a few row operations on the augmented matrix you get:

     <br />
\left[ <br />
\begin{array}{ccc|c} <br />
a&1&1&1\\ <br />
0&a-1&1-a&a(1-a)\\ <br />
1-a&0&a-1&(a-1)(a+1) <br />
\end{array} <br />
\right] <br />

    I suggest you now consider the cases a = 1 (which corresponds to infinite solutions) and a \neq 1. The case a \neq 1 might break down into two more cases, if there's another important value of a to consider ....
    a \neq 1 break down to two more cases?

    And why do it's not in row echelon form?
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  9. #9
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    Quote Originally Posted by stpmmaths View Post
    I don't want the answer to this question, just want to know what is this question want us to do? And your post is the way to tackle this question?

    By the way, I do know about Gaussian Elimination, the three types of solutions(infinite- 0=0, unique-number of equations=unknowns and none-Inconsistent).

    Besides, I do know Gauss-Jordan method, Augmented matrix, Eigenvalues and Eigenvectors.
    Then read posts #2, #6. Your question requires you to discuss the different possible solutions for al the different values of a. Simple eg. ax + y = 2, x + y = 3. a = 1 => no solution, any other value of a => unique solution.
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  10. #10
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    Quote Originally Posted by mr fantastic View Post
    Then read posts #2, #6. Your question requires you to discuss the different possible solutions for al the different values of a. Simple eg. ax + y = 2, x + y = 3. a = 1 => no solution, any other value of a => unique solution.
    Ooic, finally I get it. Thanks
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