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desalexus

  • 2 years ago

How can you determine whether a matrix product AB is defined?

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  1. Loser66
    • 2 years ago
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    @Mertsj explain him, please.

  2. Mertsj
    • 2 years ago
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    You're doing fine. Give an example. That will help.

  3. desalexus
    • 2 years ago
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    its HER and like this A is 2×3 and B is 3×2, so AB is (2×3)(3×2).

  4. RolyPoly
    • 2 years ago
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    \[A_{m\times n}B_{n\times p}\]? The number of columns of A = number of rows of B

  5. RolyPoly
    • 2 years ago
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    Dimension of AB would be m×p

  6. desalexus
    • 2 years ago
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    Thanks

  7. Mertsj
    • 2 years ago
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    It depends on the dimensions:

  8. mathmale
    • 2 years ago
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    The example that Desalexus presents is illustrative: A is 2×3 and B is 3×2, so AB is (2×3)(3×2). Note how Matrix A has 2 rows and 3 columns, and B 3 rows and 2 columns. We can indeed multiply matrices A and B (in that order).

  9. Mertsj
    • 2 years ago
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    |dw:1388979444164:dw|

  10. Mertsj
    • 2 years ago
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    |dw:1388979475429:dw|

  11. RolyPoly
    • 2 years ago
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    |dw:1388979474597:dw|

  12. mathmale
    • 2 years ago
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    Yes, Mertsj, and you can make that statement more precise by stating that "the number of columns of the first matrix must equal the number of rows of the second. RolyPoly is correct in his drawing (immediately above), whereas I found that I was wrong at the onset (and have deleted my incorrect statement accordingly)!

  13. mathmale
    • 2 years ago
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    I'd rather find my own mistakes than have someone else find them for me! :)

  14. Mertsj
    • 2 years ago
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    Sometimes it is easier for the asker to see an example than to decipher a bunch or words but it is good to have both so the asker can choose.

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