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Math Help - Matrix Inverses, help plz

  1. #1
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    Matrix Inverses, help plz

    Let A be a 4 X 2 matrix, A = \begin{bmatrix}-1&0 \\ 0 & 1 \\ 1&2\\ 2&1 \end{bmatrix}

    Is there a 2X4 matrix such that BA = I_2?

    A little clarifications would be nice, totally dont understand this question at all.
    Last edited by p00ndawg; October 19th 2008 at 06:59 PM.
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    Let A be a 4 X 2 matrix, A = \begin{bmatrix}-1&0 \\ 0 & 1 \\ 1&2\\ 2&1 \end{bmatrix}

    Is there a 2X4 matrix such that BA = I_2?

    A little clarifications would be nice, totally dont understand this question at all.
    A necessary (but not sufficient) condition for the inverse of a matrix to exist is that the matrix must be square ....
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    Quote Originally Posted by mr fantastic View Post
    A necessary (but not sufficient) condition for the inverse of a matrix to exist is that the matrix must be square ....
    I think you misunderstood the question. There is a matrix which satisfies

    The question is asking can we find a matrix which satisfies the equation and we can

    B  = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix} is one example
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    Quote Originally Posted by SimonM View Post
    I think you misunderstood the question. There is a matrix which satisfies

    The question is asking can we find a matrix which satisfies the equation and we can

    B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix} is one example
    So what's I_2 meant to represent?
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    Quote Originally Posted by mr fantastic View Post
    So what's I_2 meant to represent?
    I_2 = \left(\begin{array}{cc}1&0\\0&1\end{array}\right)

    More generally, I_n is the nxn square matrices with 1 in its leading diagonal (i.e. from top-left to bottom-right).
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    Quote Originally Posted by SimonM View Post
    I think you misunderstood the question. There is a matrix which satisfies

    The question is asking can we find a matrix which satisfies the equation and we can

    B = \begin{bmatrix} 1& -1 & 0 & 1 \\ 0 &1 & 0 &0 \end{bmatrix} is one example
    Yes, I did misunderstand the question.

    One way to do it would be to assume that B = \begin{bmatrix} a& b & c & d \\ e &f & g &h \end{bmatrix}, do the multiplication, equate entries and solve the resulting four linear equations (infinite number of solutions).
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    Quote Originally Posted by mr fantastic View Post
    Yes, I did misunderstand the question.

    One way to do it would be to assume that B = \begin{bmatrix} a& b & c & d \\ e &f & g &h \end{bmatrix}, do the multiplication, equate entries and solve the resulting four linear equations (infinite number of solutions).
    That is indeed how I did it (same letters and everything!)
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    Quote Originally Posted by SimonM View Post
    That is indeed how I did it (same letters and everything!)
    Well you know what they say about great minds ......
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  9. #9
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    Quote Originally Posted by mr fantastic View Post
    Well you know what they say about great minds ......
    ... and fools
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  10. #10
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    Quote Originally Posted by p00ndawg View Post
    Let A be a 4 X 2 matrix, A = \begin{bmatrix}-1&0 \\ 0 & 1 \\ 1&2\\ 2&1 \end{bmatrix}

    Is there a 2X4 matrix such that BA = I_2?

    A little clarifications would be nice, totally dont understand this question at all.
    By inspection one such matrix is:

    <br />
\begin{bmatrix}-1&0 &0&0\\ 0&1&0&0 \end{bmatrix}<br />

    CB
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  11. #11
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    ahhh I see thank you guys.
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