Find a basis of the column space of the matrix A 2 4 2 0 2

Find a basis of the column space of the matrix A = [2 -4 -2 0 2 -4 0 2 8 -16 -4 4].

Solution

1. Add (-1 * row_1) to row_2:

2. Add (-4 * row_1) to row_3:

3. Add (-2 * row_ 2) to row_3:

The matrix has 2 pivots

(2)

Because we have found pivots in columns 0 and 2. We know that these columns in the original matrix define the Column Space of the matrix.
Therefore, the Column Space is given by the following equation:

2	-4	-2	0
0	0	2	2
8	-16	-4	4