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Thread: Finding a corresponding matrix

  1. #1
    CBM
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    Finding a corresponding matrix

    For this question, I know that [1, 1] * [?, ?] = [-1. 3] and [1. -1]*[?,?] = [-3,7] but I am confused how to go about finding a corresponding matrix that works for both of them.
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  2. #2
    MHF Contributor
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    Re: Finding a corresponding matrix

    Let the matrix be a 2x2 matrix be A with elements a, b, c, d.

    And write the column matrices (vectors) as given (not as rows as you have).

    Multiply A (on the left) by the each of the input vectors and equate with the image vectors.

    This will give you two pairs of simultaneous equations. One pair will involve a and b, the other pair will involve c and d. Solve in the usual way.

    Let us know if that works for you.
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  3. #3
    Member Walagaster's Avatar
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    Re: Finding a corresponding matrix

    Here's a similar, but different, approach for you to try. Call your unknown matrix $A$. You are given$$
    A \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} -1 \\ 3 \end{bmatrix}\text{ and }
    A \begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} -3 \\ 7 \end{bmatrix}
    $$Expressing these two equations as a single matrix equation gives$$

    A \begin{bmatrix} 1 & 1 \\1 & -1 \end{bmatrix} = \begin{bmatrix}-1 & -3 \\ 3 & 7 \end{bmatrix}$$Now can you solve for the matrix $A$?
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