Row Echelon Form

• September 20th 2007, 03:17 PM
VenomHowell
Row Echelon Form
Solve the given systems by reducing the corresponding augmented matrix to row-echelon form. Find the rank of the matrix of coefficients.

A.) 2x + 3y + z =1
x + y + z = 3
3x + 4y + 2z = 4

I'm having a LOT of trouble reducing this one to row echelon form. Can anyone help me out a bit? The third column is being a real pain to try and reduce...

The best I've been able to get is

| 1 1 1 | 3 |
| 0 1 -1| -5|
| 0 0 0 | 0 |

I pretty much am given two unique equations with a derived one... Is there any way to actually get a more accurate answer than this? And would the rank be 2?
• September 20th 2007, 08:56 PM
Jhevon
Quote:

Originally Posted by VenomHowell
Solve the given systems by reducing the corresponding augmented matrix to row-echelon form. Find the rank of the matrix of coefficients.

A.) 2x + 3y + z =1
x + y + z = 3
3x + 4y + 2z = 4

I'm having a LOT of trouble reducing this one to row echelon form. Can anyone help me out a bit? The third column is being a real pain to try and reduce...

The best I've been able to get is

| 1 1 1 | 3 |
| 0 1 -1| -5|
| 0 0 0 | 0 |

I pretty much am given two unique equations with a derived one... Is there any way to actually get a more accurate answer than this? And would the rank be 2?

umm, it is in row-echelon form. do you mean you want to get it to reduced row-echelon form? if so:

(assuming you were correct up to this point)

$\left| \begin {array}{ccc|c} 1 & 1 & 1 & 3 \\ 0 & 1 & {-1} & 5 \\ 0 & 0 & 0 & 0 \end {array} \right|$

subtract the second row from the first, and rewrite it as the first row, we get:

$\left| \begin {array}{ccc|c} 1 & 0 & 2 & 8 \\ 0 & 1 & {-1} & 5 \\ 0 & 0 & 0 & 0 \end {array} \right|$

and yes, $rank(A) = 2 = \mbox { \# of leading 1's}$

where A, is of course, the matrix of coefficients