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Math Help - [SOLVE] Matrix problem

  1. #1
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    Question [SOLVE] Matrix problem

    Let A =
    <br />
\left|\begin{array}{cccc}2 & 1 & 1 \\ 3 & 2 & 1 \\ 1 & 1 & 1 \end{array}\right|<br />

    (a) Calculate det(A).
    (b) Use the Inversion Algorithm to compute A^(−1).
    (c) Consider a new matrix B which is the same as A except the 2 in the upper left hand corner of A is replaced by a 1. What do you say about the inverse of this new matrix?

    Is anyone can explain how to do (b) and (c) please!!! !!!!!!!

    My answer:
    (a) (2*2*1)+(1*1*1)+(1*3*1)-(1*2*1)-(2*1*1)-(1*3*1) = 1
    (b) 
    (c)
    Last edited by lin.13579; September 2nd 2009 at 04:34 PM.
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  2. #2
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    Question det and Inversion Algorithm problem

    Let A =
    <br />
\left|\begin{array}{cccc}2 & 1 & 1 \\ 3 & 2 & 1 \\ 1 & 1 & 1 \end{array}\right|<br />


    (a) Calculate det(A).
    (b) Use the Inversion Algorithm to compute A^(−1).
    (c) Consider a new matrix B which is the same as A except the 2 in the upper left hand corner of A is replaced by a 1. What do you say about the inverse of this new matrix?

    Is anyone can teach me how to do (b) and (c) please!!! !!!!!!!

    My answer:
    (a) (2*2*1)+(1*1*1)+(1*3*1)-(1*2*1)-(2*1*1)-(1*3*1) = 1
    (b) 
    (c)
    Last edited by lin.13579; September 2nd 2009 at 04:34 PM.
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  3. #3
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    Well, since this has been up for a few days, and nobody else is helping, I thought I'd pitch in and add my thoughts.. I can't help with part (b), since I'm unfamiliar with the "Inversion Algorithm". However, part (c) is pretty straight forward.

    Use the same method for finding the determinant that you used in part (a), except this time, replace element A_{11} (the two in the upper-left corner) with a 1. You'll find that the determinant is zero. A determinant of zero means that the matrix is "singular", and therefore has no inverse. I'm sure you understand (or can figure out) why that is.
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  4. #4
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    Quote Originally Posted by DJ Hobo View Post
    Well, since this has been up for a few days, and nobody else is helping, I thought I'd pitch in and add my thoughts.. I can't help with part (b), since I'm unfamiliar with the "Inversion Algorithm". However, part (c) is pretty straight forward.

    Use the same method for finding the determinant that you used in part (a), except this time, replace element A_{11} (the two in the upper-left corner) with a 1. You'll find that the determinant is zero. A determinant of zero means that the matrix is "singular", and therefore has no inverse. I'm sure you understand (or can figure out) why that is.

    easy
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  5. #5
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    the inverse of a three by three matrix A=\left(\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{  array}\right)
    is the matrix A^{-1}=\frac{1}{DetA}\left(\begin{array}{ccc}ei-fh,&fg-di,&dh-eg\\hc-bi,&ai-cg,&gb-ah\\bf-ec,&cd-af,&ae-bd\end{array}\right)
    note that the inverse of a A's element (i,j) is given by A^{-1}_{i,j}=\frac{Det\left(\begin{array}{cc}A_{(i+1)m  od3,(j+1)mod3}&A_{(i+1)mod3,(j+2)mod3}\\A_{(i+2)mo  d3,(j+1)mod3}&A_{(i+2)mod3,(j+2)mod3}\end{array}\r  ight)}{DetA}
    a very similar formula is possible for square matrices of any size
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