## anonymous one year ago Evaluate

1. anonymous

2. freckles

multiplying a 3 by 2 with a 2 by 3 will result in a 3 by 3 the inner numbers have to match then the dimensions of the product will be the exterior numbers there

3. anonymous

wait, what do you mean 3 by 2 and 2 by 3?

4. freckles

those are the dimensions of your matrices respectively

5. freckles

anyways to find the entries you do rows from the first matrix with columns of the second matrix

6. freckles

for example entry 1 will be 2(5)+0(0)

7. freckles

in general the first element in the product matrix would look like this $\left[\begin{matrix}a_{11} & a_{12} \\ a_{21} & a_{22} \\ a_{31} & a_{32}\end{matrix}\right] \cdot \left[\begin{matrix}b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23}\end{matrix}\right] \\ =\left[\begin{matrix}a_{11} \cdot b_{11}+a_{12} \cdot b_{21} & ? & ? \\ ? & ? & ? \\ ? & ? & ?\end{matrix}\right]$

8. freckles

basically we did the dot product of <a11,a12> and <b11,b21>

9. freckles

to find the first entry that is

10. freckles

|dw:1438660253075:dw|

11. anonymous

this is so confusing, omg.

12. dan815

lol

13. dan815

do u want a formula?

14. freckles

|dw:1438660316576:dw|

15. anonymous

Oh, okay okay, I get it now! Thank you!

16. freckles

https://en.wikipedia.org/wiki/Matrix_multiplication just in case I don't really want to type it all out but wikepedia already did you can see they multiplied a 3 by 2 with a 2 by 3 here look under rectanglular matrices BA

17. anonymous

Whats the formula @dan815 :)

18. freckles

already did a formula for a 3 by 2 with a 2 by 3 *

19. dan815

|dw:1438660749700:dw|