Question

write M as a product of many factors A and B.

Answer 1

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

Answer 2

ABAAB

Answer 3

I am not sure but looks worth try.

Answer 4

\[ ABAAB =
\begin{bmatrix}
1 &0 \\
0 & 1
\end{bmatrix}
\]

Answer 5

Is this matrices??-

Answer 6

yes

Answer 7

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

Answer 8

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}}

Answer 9

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.

Answer 10

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

Answer 11

woah

Answer 12

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
\[
\begin{bmatrix}
1 & 1 \\
0 & 1
\end{bmatrix}
\times
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
=
\begin{bmatrix}
a +c & b +c\\
c & d
\end{bmatrix}
\]

Answer 13

woops!! that's b+d

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

well ... i hope there is better method.

Answer 20

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

Answer 21

A(BA.AB)

Answer 22

multply by right is a linear combinations of rows

Answer 23

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.

Answer 24

that is what i did i find first row

Answer 25

first row is two times row1A+row2B

Answer 26

AB put in first 2row1+row 2

Answer 27

thanks @experimentX

Answer 28

haha .... no probs man!!