Answer to Question #156469 in Linear Algebra for Hhh

Question

(3 4 -1 1

1 _1 3 1

4 _3 11 2. Reduce to row reduced echelon form

Answer 1

$\begin{pmatrix} 3 & 4 & -1 & 1\\ 1 & -1 & 3& 1\\ 4 & -3 & 11 & 2 \end{pmatrix}$

Let's divide the 1st row by 3

$\begin{pmatrix} 1 & 4/3 & -1/3 & 1/3\\ 1 & -1 & 3& 1\\ 4 & -3 & 11 & 2 \end{pmatrix}$

From the 2nd row we have to subtract the first row; from the 3rd row we have to subtract the 4 times first row.

$\begin{pmatrix} 1 & 4/3 & -1/3 & 1/3\\ 0 & -7/3 & 10/3& 2/3\\ 0 & -25/3 & 37/3 & 2/3 \end{pmatrix}$

Let's divide the second row by -7/3

$\begin{pmatrix} 1 & 4/3 & -1/3 & 1/3\\ 0 & 1 & -10/7& -2/7\\ 0 & -25/3 & 37/3 & 2/3 \end{pmatrix}$

To the third row we have to add the second row multiplied by 25/3

$\begin{pmatrix} 1 & 4/3 & -1/3 & 1/3\\ 0 & 1 & -10/7& -2/7\\ 0 & 0 & 3/7 & -12/7 \end{pmatrix}$

Let's divide the third row by 3/7

So the answer is: $\begin{pmatrix} 1 & 4/3 & -1/3 & 1/3\\ 0 & 1 & -10/7& -2/7\\ 0 & 0 & 1 & -4 \end{pmatrix}$