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Math Help - 3x3 matrix inverse

  1. #1
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    3x3 matrix inverse

    The matrix B is given by B = \begin{pmatrix}<br />
a & 1 & 3\\ <br />
2 & 1 & -1\\ <br />
0 & 1 & 2<br />
\end{pmatrix}

    Given that B is non-singular, find the inverse matrix {B}^{-1}.
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  2. #2
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    Quote Originally Posted by BabyMilo View Post
    The matrix B is given by B = \begin{pmatrix}<br />
a & 1 & 3\\ <br />
2 & 1 & -1\\ <br />
0 & 1 & 2<br />
\end{pmatrix}

    Given that B is non-singular, find the inverse matrix {B}^{-1}.
    Set \begin{pmatrix}<br />
a & 1 & 3 & |1 & 0 & 0\\ <br />
2 & 1 & -1 & |0  & 1 & 0\\ <br />
0 & 1 & 2 & |0 & 0 & 1 <br />
\end{pmatrix}

    Now use row operations to get the left hand side in identity form.
    Your solution will be the resulting right hand side.
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  3. #3
    Super Member Anonymous1's Avatar
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    Solution:

    B ^{-1} =\begin{pmatrix}<br />
\frac{3}{3a+2} & \frac{1}{3a+2} & \frac{-4}{3a+2}\\ <br />
\frac{-4}{3a+2} & \frac{2a}{3a+2} & \frac{a+6}{3a+2}\\ <br />
\frac{2}{3a+2} & \frac{-a}{3a+2} & \frac{a-2}{3a+2}<br />
\end{pmatrix}
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  4. #4
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    Quote Originally Posted by Anonymous1 View Post
    Solution:

    B ^{-1} =\begin{pmatrix}<br />
\frac{3}{3a+2} & \frac{1}{3a+2} & \frac{-4}{3a+2}\\ <br />
\frac{-4}{3a+2} & \frac{2a}{3a+2} & \frac{a+6}{3a+2}\\ <br />
\frac{2}{3a+2} & \frac{-a}{3a+2} & \frac{a-2}{3a+2}<br />
\end{pmatrix}
    but some how the answer for a=-1
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  5. #5
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    What do you mean???.. u asked for the inverse and the inverse that is given is correct.
    Quote Originally Posted by BabyMilo View Post
    but some how the answer for a=-1
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  6. #6
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    Quote Originally Posted by Dreamer78692 View Post
    What do you mean???.. u asked for the inverse and the inverse that is given is correct.
    unfortunately the mark scheme did not include, this question for some reason.

    but in the examiner comment, it says a=-1

    and this would be support by iii) if you use a=-1.

    thanks for the help.
    Attached Thumbnails Attached Thumbnails 3x3 matrix inverse-2.jpg  
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  7. #7
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    Quote Originally Posted by BabyMilo View Post
    unfortunately the mark scheme did not include, this question for some reason.

    but in the examiner comment, it says a=-1

    and this would be support by iii) if you use a=-1.

    thanks for the help.
    The inverse given in post #3 is correct. You are meant to use it to answer part (iii). When a = -1, B corresponds to the coefficient matrix of the given linear system ....
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