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Math Help - Solve for A

  1. #1
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    Solve for A

    hello,

    Can someone please help me with this problem?

    (I+2A)^-1 = [ -1 2 ]
    [ 4 5 ]

    not sure how to make a matrix...

    it's suppose to be a 2 x 2 matrix with row 1 = -1, 2 and row 2 = 4, 5

    Thanks!
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  2. #2
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    Quote Originally Posted by l flipboi l View Post
    hello,

    Can someone please help me with this problem?

    (I+2A)^-1 = [ -1 2 ]
    [ 4 5 ]

    not sure how to make a matrix...

    it's suppose to be a 2 x 2 matrix with row 1 = -1, 2 and row 2 = 4, 5

    Thanks!
    (I+2A)^{-1}=\begin{pmatrix}\!\!-1&2\\4&5\end{pmatrix}\Longleftrightarrow I+2A=\begin{pmatrix}\!\!-1&2\\4&5\end{pmatrix}^{-1}=\begin{pmatrix}\!\!-5/13&2/13\\4/13&1/13\end{pmatrix}\Longleftrightarrow

    2A=\begin{pmatrix}\!\!-18/13&2/13\\4/13&\!\!-12/13\end{pmatrix} ...and now divide by 2 and find your matrix.

    Note that at the end you must check that I+2A is actually invertible, otherwise the problem's no solution.

    Tonio
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  3. #3
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    Thanks!

    What i'm stumped with is I, what do you have to do with it?

    from the looks of it, since the matrix for the identity is row 1 = [1 0] row 2 = [0 1]
    just subtract 1? when you move the I to the right side?
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  4. #4
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    Quote Originally Posted by l flipboi l View Post
    Thanks!

    What i'm stumped with is I, what do you have to do with it?

    from the looks of it, since the matrix for the identity is row 1 = [1 0] row 2 = [0 1]
    just subtract 1? when you move the I to the right side?

    You have to do is substraction of matrices...you should know this if your dealing with this problem.

    Tonio
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