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Why didn't the third row change - Linear Algebra

Hi.

I have two question.
1. Why does he use the first row as the pivot row. Why not the third or the second? 4:42
2. Why did he left the third row unchanged? 5:13

http://www.youtube.com/watch?v=QVKj3LADCnA

/ Thanks
Because the first steps in the elimination process are to produce

100\begin{matrix} 1 \\0 \\0 \end{matrix}

in the first column.

Since the first element is the only non-zero one, it has to be the pivot.

No work is required on row 3, as its first element is already 0.
Reply 2
Avatar for Persson121
Persson121
OP
Original post by ghostwalker
Because the first steps in the elimination process are to produce

100\begin{matrix} 1 \\0 \\0 \end{matrix}

in the first column.

Since the first element is the only non-zero one, it has to be the pivot.

No work is required on row 3, as its first element is already 0.


Is it always to produce this at first?
100\begin{matrix} 1 \\0 \\0 \end{matrix}

Ok. If the first element was like 3 it will be then the third row will be like this.

3(1) - 3 = 0
3(2) - 4 = 2
3(1) - 1 = 5

The hole matrix will be:
1 2 1
0 2 -2
0 2 5
Original post by Persson121
Is it always to produce this at first?
100\begin{matrix} 1 \\0 \\0 \end{matrix}


That is what you're aiming for, yes.


Ok. If the first element was like 3 it will be then the third row will be like this.

3(1) - 3 = 0
3(2) - 4 = 2
3(1) - 1 = 5

The hole matrix will be:
1 2 1
0 2 -2
0 2 5


If the first element of the third row is 3, giving (3,4,1)

then you'd need to subtract 3 multiples of the first row to get zero in that first column of the third row, yielding

3-3(1) = 0
4-3(2) = -2
1-3(1)= -2

and your last row becomes (0, -2, -2)
Reply 4
Avatar for Persson121
Persson121
OP
Original post by ghostwalker
That is what you're aiming for, yes.



If the first element of the third row is 3, giving (3,4,1)

then you'd need to subtract 3 multiples of the first row to get zero in that first column of the third row, yielding

3-3(1) = 0
4-3(2) = -2
1-3(1)= -2

and your last row becomes (0, -2, -2)


Ok. Then i know that the first i gonna do if i want to "eliminate" the rows. Get 0 at the rest of the first elements at the all rows, exept the first row at.

Is it that why he call the first number at first row at pivot?
Original post by Persson121

Is it that why he call the first number at first row at pivot?


I'm finding it difficult to follow your writing.

Far as I can tell from wiki (as I don't use the term myself), a pivot is a position that corresponds to a "1" in the reduced matrix.

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