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Math Help - h such that the matrix is augmented...

  1. #1
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    h such that the matrix is augmented...

    Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system?

    1 h 2
    5 20 8

    Ok so I got 2h cannot = - 20
    Then divide by 2 and got h cannot equal = -10?

    Is this correct?
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  2. #2
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    Re: h such that the matrix is augmented...

    Quote Originally Posted by Oldspice1212 View Post
    Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system?

    1 h 2
    5 20 8

    Ok so I got 2h cannot = - 20
    Then divide by 2 and got h cannot equal = -10?
    Is this correct?

    No it is not correct.

    You need the matrix \left[ {\begin{array}{*{20}c}   1 & h  \\   5 & {20}  \\ \end{array} } \right] to be non-singular, determinate not zero.
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  3. #3
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    Re: h such that the matrix is augmented...

    I have to make it into a

    1 0
    0 1

    Is that what you mean?
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  4. #4
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    Re: h such that the matrix is augmented...

    Quote Originally Posted by Oldspice1212 View Post
    I have to make it into a

    1 0
    0 1

    Is that what you mean?

    No you must have (1)(20)-(5)(h)\ne 0~.
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  5. #5
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    Re: h such that the matrix is augmented...

    Ooh haha I got -4, does it look correct now?
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    Re: h such that the matrix is augmented...

    Quote Originally Posted by Oldspice1212 View Post
    Ooh haha I got -4, does it look correct now?
    No that is not correct.
    And I think that you are just guessing.
    Read the question. If you understand the process, then the answer is easy.
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  7. #7
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    Re: h such that the matrix is augmented...

    Its 4 since (20-5h)x2=-2
    So it's a augmented matrix of a consistant linear system if h cannot = 4?
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  8. #8
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    Re: h such that the matrix is augmented...

    Hello, Oldspice1212!

    Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.

    . . \left[\begin{array}{cc|c} 1&h&2 \\ 5&20&8 \end{array}\right]

    The system is consistent if its determinant is not equal to zero.

    If D = 0, we have: . \begin{vmatrix}1&h \\ 5&20\end{vmatrix} \:=\:0

    . . Hence: . 20 - 5h \:=\:0 \quad\Rightarrow\quad h \:=\:4


    \text{The system is consistent for all }h \ne 4.
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  9. #9
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    Re: h such that the matrix is augmented...

    ^ yup I got it, thanks guys
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