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Math Help - Matrix

  1. #1
    Senior Member
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    Matrix

    Hello i got a problem!
    ima decide a inverkar to this Matrix A=1 0 -1 1 an it says clue ima set B= x y z tand decide x,y,z,t, for B shall be inverse to A.( its 2x2 the first 2 number are the number on top and the last 2 is at bottom idk what u say on english

    Its a 2x2 Matrix sorry for not writing it with latex and sorry for My bad english.
    So i did AB and get C= 1x 1y, -1x+z, -1y+1t
    idk why i did not write as t insted of having one before byt hope u guys did understand and looking forward to se all help
    Attached Thumbnails Attached Thumbnails Matrix-image.jpg  
    Last edited by Petrus; November 23rd 2012 at 04:55 AM.
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  2. #2
    MHF Contributor
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    Re: Matrix

    Hey Petrus.

    Do you just want to find the inverted matrix of A given what is written in the attachment?

    If the answer is yes, here is the Octave output for this problem:

    >> A = [1, 0; -1, 1]
    A =

    1 0
    -1 1

    >> inv(A)
    ans =

    1 0
    1 1
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  3. #3
    MHF Contributor

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    Re: Matrix

    suppose we want to invert:

    A = \begin{bmatrix}1&0\\-1&1 \end{bmatrix}

    your clue says to set:

    B = \begin{bmatrix}x&y\\z&t \end{bmatrix}.

    so we calculate:

    AB = \begin{bmatrix} x&y\\z-x&t-y \end{bmatrix}

    if B is to be the inverse of A, we must have AB = I.

    thus:

    x = 1
    y = 0
    z - x = 0
    t - y = 1

    from z - 1 = 0, we get z = 1.
    from t - 0 = 1, we get t = 1.

    thus:

    A^{-1} = B = \begin{bmatrix}1&0\\1&1 \end{bmatrix}
    Thanks from Petrus
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