anonymous 2 years ago How can you determine whether a matrix product AB is defined?

1. Loser66

2. Mertsj

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

3. anonymous

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

4. anonymous

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

5. anonymous

Dimension of AB would be m×p

6. anonymous

Thanks

7. Mertsj

It depends on the dimensions:

8. 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).

9. Mertsj

|dw:1388979444164:dw|

10. Mertsj

|dw:1388979475429:dw|

11. anonymous

|dw:1388979474597:dw|

12. 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)!

13. mathmale

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

14. 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.