anonymous
  • anonymous
How can you determine whether a matrix product AB is defined?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Loser66
  • Loser66
@Mertsj explain him, please.
Mertsj
  • Mertsj
You're doing fine. Give an example. That will help.
anonymous
  • anonymous
its HER and like this A is 2×3 and B is 3×2, so AB is (2×3)(3×2).

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anonymous
  • anonymous
\[A_{m\times n}B_{n\times p}\]? The number of columns of A = number of rows of B
anonymous
  • anonymous
Dimension of AB would be m×p
anonymous
  • anonymous
Thanks
Mertsj
  • Mertsj
It depends on the dimensions:
mathmale
  • mathmale
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).
Mertsj
  • Mertsj
|dw:1388979444164:dw|
Mertsj
  • Mertsj
|dw:1388979475429:dw|
anonymous
  • anonymous
|dw:1388979474597:dw|
mathmale
  • mathmale
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)!
mathmale
  • mathmale
I'd rather find my own mistakes than have someone else find them for me! :)
Mertsj
  • Mertsj
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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