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sloppycanada

  • one year ago

Rules of matrices I don't understand this multiply matrices thing, what is required for me to be able to do this?

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  1. anonymous
    • one year ago
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    for the multiplication to be "legal"?

  2. sloppycanada
    • one year ago
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    Yeah I guess? Particularly for uneven matrices like say A = 5x4 and B = 4x3 That sort of thing.

  3. anonymous
    • one year ago
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    stolen from wikipedia but the product AB is defined only if the number of columns in A is equal to the number of rows in B

  4. anonymous
    • one year ago
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    for example if A was 3x2 and B was 2x3 it'd be defined if A was 3x3 and B was 2x2 it wouldn't be defined

  5. sloppycanada
    • one year ago
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    So 5x4 and 4x3 wouldn't work?

  6. anonymous
    • one year ago
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    look at the inner most numbers the way matrices are expressed it's rowx col

  7. anonymous
    • one year ago
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    so \(axb * cxd\) is defined when b=c

  8. anonymous
    • one year ago
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    this is part of why matrix multiplication also isn't commutative for example, 2x2 * 1x2 isn't defined but 2x1 * 2x2 is defined

  9. anonymous
    • one year ago
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    and the outer numbers tells you the size of the product matrix. So a 2x1 * 2x2 multiplication will result in a 2x2 matrix and 5x4 * 4x3 gives a 5x3 matrix

  10. anonymous
    • one year ago
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    The number of columns of the left matrix must equal the rows of the right matrix.

  11. anonymous
    • one year ago
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    Matrices come from systems of equations. For example: \[ ax+by = e\\ cx+dy=f \]We can write this a vector equation: \[ \begin{bmatrix}a\\c\end{bmatrix}x+\begin{bmatrix}b\\d\end{bmatrix}y=\begin{bmatrix}e\\f\end{bmatrix} \]However, if we want to treat the variables \(x\) and \(y\) as components of a vector, then we need matrix multiplication to be defined to work this way:\[ \begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}ax+by\\cx+dy\end{bmatrix} \]This way we can say: \[ \begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}e\\f \end{bmatrix} \]

  12. sloppycanada
    • one year ago
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    Okay... but 5x4 and 4x3 will work.

  13. anonymous
    • one year ago
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    Matrices are denoted with rows by columns. If the left matrix has 4 columns, and the right matrix has 4 rows, then it should work.

  14. sloppycanada
    • one year ago
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    And we have 4 columns and 4 rows.

  15. sloppycanada
    • one year ago
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    Which means this is possible, right?

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