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Thread: Matrix questions

  1. #1
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    Matrix questions

    How can I calculate the X and AX?
    Matrix questions-33522857_2194891377194974_8715196505733988352_n.jpg
    Thank you so much, your help!!
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  2. #2
    Senior Member x3bnm's Avatar
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    Re: Matrix questions

    Matrix multiplication:

    $\displaystyle \left[\begin{matrix} 1 & 2 & 3\\
    4 & 5 & 6\\
    7 & 8 & 9\end{matrix}\right]\left[\begin{matrix} 1 & 2 & 3\\
    4 & 5 & 6\\
    7 & 8 & 9\end{matrix}\right]$



    $\displaystyle =\left[\begin{matrix} (1 * 1) + (2 * 4) + (3 * 7) & (1 * 2) + (2 * 5) + (3 * 8) & (1 * 3) + (2 * 6) + (3 * 9)\\
    (4 * 1) + (5 *4) + (6 * 7) & (4 * 2) + (5 * 5) + (6 * 8) & (4 * 3) + (5 * 6) + (6 * 9)\\
    (7 * 1) + (8 * 4) + (9 * 7) & (7 * 2) + (8 * 5) + (9 * 8) & (7 * 3) + (8 * 6) + (9 * 9)\end{matrix}\right]$



    $\displaystyle =\left[\begin{matrix}30 & 36 & 42\\
    66 & 81 & 96\\
    102 & 126 & 150\end{matrix}\right] $



    For more information you can take a look at step by step multiplication at Matrix Multiplication Calculator

    And solving linear equations using Gauss Jordan elimination method you can look at Gauss-Jordan Elimination Calculator
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  3. #3
    MHF Contributor

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    Re: Matrix questions

    You can multiply $\displaystyle \begin{bmatrix}1 & 2 & -1 \\ 4 & -4 & 3 \\ -2 & 0 & 1 \end{bmatrix}\begin{bmatrix}1 & 1 & 3 \\ 4 & 2 & 3 \\ 1 & 1 & 1 \end{bmatrix}=$$\displaystyle \begin{bmatrix}1(1)+ 2(4)- 1(1) & 1(1)+ 2(2)- 1(1) & 1(3)+ 2(3)- 1(1) \\ 4(1)- 4(4)+ 3(1) & 4(1)- 4(2)+ 3(1) & 4(3)- 4(3)+ 3(1) \\ -2(1)+ 0(4)+ 1(1) & -2(1)+ 0(2)+ 1(1) & -2(3)+ 0(3)+ 1(1)\end{bmatrix}=$$\displaystyle \begin{bmatrix} 8 & 4 & 8 \\ 9 & -1 & 3 \\ -1 & -1 & -5 \end{bmatrix}$.

    However, it is impossible to multiply that 3 by 3 matrix by the "1 by 4" matrix $\displaystyle \begin{bmatrix}x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}$ so there is NO "X" and so NO "AX".
    Last edited by HallsofIvy; Jun 30th 2018 at 07:02 AM.
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