Question

Find the echelon form of this augmented matrix

Answer 1

Answer:

See the explanation

Step-by-step explanation:

If we want to find the row echelon form of a given matrix, then it should have the following properties:

• The first non zero element in each row, which is also known as the leading entry, should be 1
• Each leading entry is in the column to the right of the leading entry in the previous row
• If any rows have all zero elements, are placed below the rown with non zero elements.

$\left[\begin{array}{cccc}1&3&-2&400\\-1&-2&-1&-100\\-1&-1&-3&700\end{array}\right]$

Add 1 times the 1st row into 2nd row

$\left[\begin{array}{cccc}1&3&-2&400\\0&1&-3&300\\-1&-1&-3&700\end{array}\right]$

Add 1 time the 1st row into 3rd row

$\left[\begin{array}{cccc}1&3&-2&400\\0&1&-3&300\\0&2&-5&1100\end{array}\right]$

Add -2 times the 2nd row into 3rd row.

$\left[\begin{array}{cccc}1&3&-2&400\\0&1&-3&300\\0&0&1&500\end{array}\right]$