Consider the matrix A 2 1 1 0 4 2 1 2 6 3 2 2 Determine a m

Consider the matrix A = (2 1 1 0 4 2 1 2 6 3 2 2) Determine a maximal linearly independent subset of columns from A.

Solution

We will reduce A to its RREF as under:

Multiply the 1st row by ½

Add -4 times the 1st row to the 2nd row

Add -6 times the 1st row to the 3rd row

Multiply the 2nd row by -1

Add 1 times the 2nd row to the 3rd row

Add -1/2 times the 2nd row to the 1st row

Then the RREF of A is

1

½

0

1

0

0

1

-2

0

0

0

0

Apparently, only the 1^st and the 3^rd columns of A are linearly independent. Therefore, the maximal linearly independent subset of columns from A is { (2,4,6)^T, (1,1,2)^T}

1	½	0	1
0	0	1	-2
0	0	0	0