I want to solve a problem with just numbers from 0 to 2, how do I do that?

I'm doing a homework that consists of making a matrix according to these steps:

t= [0;1;2]
A= [1;1;0];
B= [1;1;1];
C= [0;1;1];
M= [A B C t]
sol= rref(M)

The thing is that I want to get a matrix that gives me values from 0 to 2. However, I don't get the correct answer since it gives me this:

sol =

     1     0     0     1
     0     1     0     1
     0     0     1     1

Correct answer:

sol =

     1     0     0     2
     0     1     0     1
     0     0     1     1

[the cyclist]

MATLAB gives

sol =

     1     0     0    -1
     0     1     0     1
     0     0     1     1

right?

[Roberto García Morones]

Yes, I forgot to put abs(rref(M))

Answer 1

[the cyclist]

Are you sure you copied everything from the assignment correctly? Can you post the text of the assignment here?

I did the Gauss-Jordan elimination with partial pivoting by hand, and get same result as MATLAB.

[Roberto García Morones]

It is in Spanish but I translated it in English:

Consider a row with only three lights, each of which can be off, light blue, or dark blue. Below the lights are three switches, A, B, and C, each of which changes the particular light states to the next state, in the order shown in the figure.Switch A changes the states of the first two lights; switch B, the three lights; and switch C, the last two lights. If all three lights are initially off, is it possible to press the switches in a certain order so that the lights are off, light blue and dark blue, in that order?

A= [1;1;0]

B= [1;1;1]

C= [0;1;1]

t= [0;1;2]

I added an image that says in the first part is the matrix as a whole and then the matrix solved with Gauss-Jordan

[the cyclist]

I think the fact that MATLAB gives a -1 is important, and you do not want to take the absolute value after rref().

I also think the fact that

mod(-1,3) == 2

is important, since the lights have 3 positions.

Does that help?

[Roberto García Morones]

A little bit, in your case how would you code it so it gives me this solution?

sol =

1 0 0 2

0 1 0 1

0 0 1 1

[Roberto García Morones]

Nevermind, I already did it. Thank you so much!