## RaphaelFilgueiras Group Title write M as a product of many factors A and B. one year ago one year ago

1. RaphaelFilgueiras Group Title

|dw:1348860718372:dw|

2. RaphaelFilgueiras Group Title

i already did it ,but i want to know how to do it with a systematic way,thanks

3. RaphaelFilgueiras Group Title

ABAAB

4. experimentX Group Title

I am not sure but looks worth try.

5. experimentX Group Title

$ABAAB = \begin{bmatrix} 1 &0 \\ 0 & 1 \end{bmatrix}$

6. bthemesandtricks Group Title

Is this matrices??-

7. RaphaelFilgueiras Group Title

yes

8. RaphaelFilgueiras Group Title

A.B.A.A.B=M for sure

9. experimentX Group Title

hold on ... looks I'm doing wrong calculation with MMA http://www.wolframalpha.com/input/?i={{1%2C+0}%2C+{1%2C+1}}*{{a%2C+b}%2C+{c%2C+d}}

10. experimentX Group Title

http://www.wolframalpha.com/input/?i={{1%2C+1}%2C+{0%2C+1}}*{{a%2C+b}%2C+{c%2C+d}} let's begin with the nature of those transformations.

11. experimentX Group Title

Indeed it workds ...i had been using * where i should have used .

12. bthemesandtricks Group Title

woah

13. experimentX Group Title

let's begin with the nature of transformation $\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} \times \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} a & b \\ a+ c & b+d \end{bmatrix}$ and $\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} \times \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} a +c & b +c\\ c & d \end{bmatrix}$

14. experimentX Group Title

woops!! that's b+d

15. experimentX Group Title

$M = \begin{bmatrix} 3 & 4 \\ 3 + 2 & 4+3 \end{bmatrix}$ so you need to preceed the left to right by 1

16. klimenkov Group Title

Try to write the expressions for multiplying this matrices from another side.

17. experimentX Group Title

A adds to the bottom while B adds to top. since 4>3 let's looks for B.A = {{2, 1}, {1, 1}} A.B = {{1, 1}, {1, 2}} so A.B is our choice

18. experimentX Group Title

add down {{1, 1}, {2, 3}} add up {{3, 4}, {2, 3}} add down {{3, 4}, {5, 7}}

19. RaphaelFilgueiras Group Title

i did it in a similar way but without using equations too

20. experimentX Group Title

well ... i hope there is better method.

21. RaphaelFilgueiras Group Title

|dw:1348863383528:dw|

22. RaphaelFilgueiras Group Title

too mantain the first line and add to second i have to multlyby A

23. RaphaelFilgueiras Group Title

A(BA.AB)

24. RaphaelFilgueiras Group Title

multply by right is a linear combinations of rows

25. experimentX Group Title

well ... i kept fitting up. if you intoduce difference and use that difference to introduce another difference .. then it would be (2d) double step. so keep adding from 1, 1 (no difference) to 1 2 .... until the difference is able to give exact value at top. and use that difference to create double difference at bottom.

26. RaphaelFilgueiras Group Title

that is what i did i find first row

27. RaphaelFilgueiras Group Title

first row is two times row1A+row2B

28. RaphaelFilgueiras Group Title

AB put in first 2row1+row 2

29. RaphaelFilgueiras Group Title

thanks @experimentX

30. experimentX Group Title

haha .... no probs man!!