1. ## Basic Question Matrices

http://www.numbertheory.org/book/mp103.pdf

On page 12 of the book I'm stumped.

It says that the 'column numbers in which the leading entries 1 occurs' are denoted by $\displaystyle c_1,c_2,...c_r$, where r is the number of nonzero rows.

They give an example, where r=3, which means there are 3 non-zero rows in the matrix (as far as I can tell). Then the give some values for the c's. I undersatnd how the obtained the first 3 values:

$\displaystyle c_1=2$,$\displaystyle c_2=4$,$\displaystyle c_3=5$.

However, I don't see how they obtained values for $\displaystyle c_4,c_5$ and $\displaystyle c_6$.

http://www.numbertheory.org/book/mp103.pdf

On page 12 of the book I'm stumped.

It says that the 'column numbers in which the leading entries 1 occurs' are denoted by $\displaystyle c_1,c_2,...c_r$, where r is the number of nonzero rows.

They give an example, where r=3, which means there are 3 non-zero rows in the matrix (as far as I can tell). Then the give some values for the c's. I undersatnd how the obtained the first 3 values:

$\displaystyle c_1=2$,$\displaystyle c_2=4$,$\displaystyle c_3=5$.

However, I don't see how they obtained values for $\displaystyle c_4,c_5$ and $\displaystyle c_6$.
I think the answer is in the text?

"denote the column numbers in which the leadingentries 1 occur"

That's what you got so far - it is column 2,4 and 5

so $\displaystyle c_1 = 2, c_2 = 4$ and $\displaystyle c_3 = 5$

There are three columns remaining, right?

So $\displaystyle c_4 = (column \ nr.) 1$

$\displaystyle c_5 = (column \ nr.) 3$

$\displaystyle c_6 = (column \ nr.) 6$

In the essay: "the R E M A I N I N G column numbers being denoted by $\displaystyle c_{r+1},...,c_n$"

[there are 6 columns, so every $\displaystyle c_i$ = a different column number , i =1,2,3,4,5,6]

Do you see it now?

Yours
Rapha