## desalexus Group Title How can you determine whether a matrix product AB is defined? 8 months ago 8 months ago

1. Loser66 Group Title

@Mertsj explain him, please.

2. Mertsj Group Title

You're doing fine. Give an example. That will help.

3. desalexus Group Title

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

4. RolyPoly Group Title

$A_{m\times n}B_{n\times p}$? The number of columns of A = number of rows of B

5. RolyPoly Group Title

Dimension of AB would be m×p

6. desalexus Group Title

Thanks

7. Mertsj Group Title

It depends on the dimensions:

8. mathmale Group Title

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 Group Title

|dw:1388979444164:dw|

10. Mertsj Group Title

|dw:1388979475429:dw|

11. RolyPoly Group Title

|dw:1388979474597:dw|

12. mathmale Group Title

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 Group Title

I'd rather find my own mistakes than have someone else find them for me! :)

14. Mertsj Group Title

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.