Finding the Echelon Form of a Matrix Example 1

Example 1

In this example we will find the echelon form of the matrix

\[A = \begin{bmatrix} 1 & 2 & 3 & 1\\ 2 & 3 & 3 & 3\\ 3 & 10 & 12 & 12 \end{bmatrix}\]

A = matrix([[1, 2, 3, 1],\
            [2, 3, 3, 3],\
            [3,10,12,12]])

The first step will subtracting twice the first row to the second (R2 - 2\(\times\) R1).

IMPORTANT NOTE 1: When performing row operations, the original matrix is lost.

IMPORTANT NOTE 2: Remember that indexing starts at 0.

A.add_multiple_of_row(1,0,-2)

A

[ 1  2  3  1]
[ 0 -1 -3  1]
[ 3 10 12 12]

Then we subtract three times the first row to the third (R3-3\(\times\)R1)

A.add_multiple_of_row(2,0,-3)

If we look at the matrix A we can see how it changed:

A

[ 1  2  3  1]
[ 0 -1 -3  1]
[ 0  4  3  9]

A.add_multiple_of_row(2,1,4)

Inspecting the matrix A we can see the final result.

A

[ 1  2  3  1]
[ 0 -1 -3  1]
[ 0  0 -9 13]