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Math Help - find c value that matrix is not invertible

  1. #1
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    find c value that matrix is not invertible

    I am trying to solve this, but I am stuck....

    1 2 -1
    2 3 c
    0 c -15


    1 2 -1
    0 -1 (2+c)
    0 c -15


    1 2 -1
    0 1 (-2)-c))
    0 1/15c 1

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  2. #2
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    Re: find c value that matrix is not invertible

    Quote Originally Posted by mathproblems View Post
    I am trying to solve this, but I am stuck....
    1 2 -1
    2 3 c
    0 c -15

    Expand and solve for c~.

    \left| {\begin{array}{rr}   3 & c  \\   c & { - 15}  \\\end{array} } \right| - 2\left| {\begin{array}{rr}   2 & { - 1}  \\   c & { - 15}  \\\end{array} } \right|=0
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  3. #3
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    Re: find c value that matrix is not invertible

    Thank you

    am I doing it correctly?

    -45-c^2 - 2 (-30 - (-1) -c)) = 0

    what shall I do next?
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  4. #4
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    Re: find c value that matrix is not invertible

    Your expansion of the second det is incorrect.
    -45 - c^2 -2(-30 +c) = 0

    Solve this quadratic equation to get the values of c. (c should be -5 and 3)
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  5. #5
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    Re: find c value that matrix is not invertible

    Hello, mathproblems!

    Your method should work if you know what to look for.
    (But from your responses, I'm not sure you do.)


    \text{Find }c\text{ so that A is not invertible: }\;A \;=\;\begin{vmatrix}1&2&\text{-}1 \\ 2&3&c \\ 0&c&\text{-}15 \end{vmatrix}

    We have: . \left|\begin{array}{ccc}1&2&\text{-}1 \\ 2&3&c \\ 0&c&\text{-}15 \end{array}\right|

    \begin{array}{c} \\ R_2-2R_1 \\ \\ \end{array}\left|\begin{array}{ccc}1&2&\text{-}1 \\ 0&\text{-}1&c\!+\!2 \\ 0&c&\text{-}15 \end{array}\right|

    \begin{array}{c}R_1+2R_2 \\ \\ R_3+c\!\cdot\!R_2 \end{array}\left|\begin{array}{ccc} 1&0&2c+3 \\ 0&\text{-}1 & c+2 \\ 0&0& c^2\!+\!2c\!-\!15 \end{array}\right|


    A matrix is not invertible if an entire row is composed of zeros.

    That is: . c^2+2c-15 \:=\:0 \quad\Rightarrow\quad (x-3)(x+5) \:=\:0

    Therefore: . c \,=\,3,\,\text{-}5
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