# row reduced augmented matrix

#### Sonarks

##### New member
Thought i knew how to use Gaussian elimination to find the row echelon form but i just cant seem to get the answer the attached question is looking for in part b. Can someone pleaseeeeeee help

#### MarkFL

##### Super Moderator
Staff member
Hello, and welcome to FMH!

#### Sonarks

##### New member
Hello, and welcome to FMH!

(a) $$\displaystyle \left[\begin{array}{c}1 & 2 & -1 & -3 \\ 3 & 5 & k & -4 \\ 9 & k+13 & 6 & 9 \end{array}\right]$$

(b) $$-3R_1+R_2$$

$$\displaystyle \left[\begin{array}{c}1 & 2 & -1 & -3 \\ 0 & -1 & k+3 & 5 \\ 9 & k+13 & 6 & 9 \end{array}\right]$$

$$-R_2$$

$$\displaystyle \left[\begin{array}{c}1 & 2 & -1 & -3 \\ 0 & 1 & -k-3 & -5 \\ 9 & k+13 & 6 & 9 \end{array}\right]$$

$$-9R_1+R_3$$

$$\displaystyle \left[\begin{array}{c}1 & 2 & -1 & -3 \\ 0 & 1 & -k-3 & -5 \\ 0 & k-5 & 15 & 36 \end{array}\right]$$

$$-(k-5)R_2+R_3$$

$$\displaystyle \left[\begin{array}{c}1 & 2 & -1 & -3 \\ 0 & 1 & -k-3 & -5 \\ 0 & 0 & k^2-2k & 5k+11 \end{array}\right]$$
Thank you so much