1. ## Elementary row operations

Ok, here is one of the questions I have. I have several but I will just do one at a time. Please reply if you can help me with steps or answer or anything. Like I said, I am new at this but I thought it might be helpful. Thanks in advance for the help.

Use Elementary row operations to write the matrix in echelon form:

[2 4 2 6]
[-2 1 3 4]
[3 2 1 5]

If you know that answer, that is great, I am just really stumped on this weeks work.

Kasey

2. Hello, Kasey!

Use Elementary row operations to write the matrix in echelon form:

. . $\begin{bmatrix}\; 2 & 4 & 2 & | & 6 \;\\ \;\text{-}2 & 1 & 3 &|& 4\;\\
\;3 & 2 & 1 &|& 5\; \end{bmatrix}$

$\begin{array}{c}R_1+R_2 \\ R_2 + R_3 \\ \\ \end{array}\;
\begin{bmatrix}\;0 & 5 & 5 &|& 10 \;\\ \;1 & 3 & 4 &|&9 \;\\ \;3 & 2 & 1 &|&5\; \end{bmatrix}$

$\begin{array}{c}\text{Switch} \\ R_1 \:\&\:R_2 \\ \\ \end{array}\;
\begin{bmatrix}\;1 & 3 & 4 &|& 9\; \\ \;0 & 5 & 5 &|& 10\; \\ \;3 & 2 & 1 &|& 5\;\end{bmatrix}$

$\begin{array}{c}\\ \frac{1}{5}\!\cdot\!R_2 \\ R_3-3R_1\end{array}\;
\begin{bmatrix}\;1 & 3 & 4 &|& 9\; \\ \;0 & 1 & 1 &|& 2\; \\ \;0 & \text{-}7 & \text{-}11 &|& \text{-}22\; \end{bmatrix}$

$\begin{array}{c}R_1-3R_2 \\ \\ R_3+7R_2\end{array}\;
\begin{bmatrix}\;1 & 0 & 1 &|& 3\; \\ \;0 & 1 & 1 &|& 2\; \\ \;0 & 0 & \text{-}4 &|& \text{-}8\;\end{bmatrix}$

. . $\begin{array}{c}\\ \\ \text{-}\frac{1}{4}R_3\end{array}\;
\begin{bmatrix}\;1 & 0 & 1 &|& 3\; \\ \;0 & 1 & 1 &|& 2\; \\ \;0 & 0 & 1 &|&2\;\end{bmatrix}$

$\begin{array}{c}R_1-R_3 \\ R_2-R_3 \\ \end{array}\;
\begin{bmatrix}\;1 & 0 & 0 &|& 1\; \\ \;0 & 1 & 0 &|& 0\; \\ \;0 & 0 & 1 &|& 2\;\end{bmatrix}$