Question

-1 3 2
A= 3 -9 -6
-3 9 6
.

Find a basis of A.

Answer 1

If you divide the first row by -1, the second row by 3, and the third row by -3, we reduce matrix A to
1 -3 -2
1 -3 -2
1 -3 -3. Its row-echelon form is

1 -3 -2
0 0 0
0 0 0.

Therefore, a basis for the one-dimensional vector space that is the image of the transformation A from R^3 to R is the column vector
[1, -3, -2]^T.

Answer 2

WHAT IF WE ARE TRYING TO FIND THE BASIS OF NULLSPACE(A) ? :D

Answer 3

Finding a basis for the nullspace is equivalent to solving a system of equations.
Ax = 0 find the set of all x that satisfies it.