Question

find the reduced echelon form of [1, 2, 4; 0, 3, 6; 0, 2, 4]

Answer 1

Answer:

$\begin{pmatrix}1&0&0\\0&3&6\\0&0&0 \end{pmatrix}$

Step-by-step explanation:

Given:

$\begin{pmatrix}1&2&4\\0&3&6\\0&2&4 \end{pmatrix}$

We need to reduce the given matrix to reduced echelon form.

Solution:

Make zeroes in column 1 except the entry at row 1, column 1. As we can see all elements in column are already zero. Make zeroes in column 2 except the entry at row 2, column 2.

$\begin{pmatrix}1&2&4\\0&3&6\\0&2&4 \end{pmatrix}\\R_3\rightarrow R_3-\frac{2}{3}R_2\\\begin{pmatrix}1&2&4\\0&3&6\\0&0&0 \end{pmatrix}\\R_2\rightarrow \frac{R_2}{3}\\\begin{pmatrix}1&2&4\\0&1&2\\0&0&0 \end{pmatrix}\\R_1\rightarrow R_1-2R_2\\\begin{pmatrix}1&0&0\\0&3&6\\0&0&0 \end{pmatrix}$

So, $\begin{pmatrix}1&2&4\\0&3&6\\0&2&4 \end{pmatrix}$ in reduce echelon form is $\begin{pmatrix}1&0&0\\0&3&6\\0&0&0 \end{pmatrix}$