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imotive
-1 3 2 A= 3 -9 -6 -3 9 6 . Find a basis of A.
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.
WHAT IF WE ARE TRYING TO FIND THE BASIS OF NULLSPACE(A) ? :D
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.