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The null space contains every vector A maps to zero. Row reducing exposes the free columns, and setting each free variable to 1 in turn generates a basis. Rank plus nullity always equals the number of columns.
Rank-nullity theorem
rank(A) + nullity(A) = number of columns
The second row is twice the first, so the rank is 1 and the nullity is 2.
When the rank equals the number of columns, meaning the columns are linearly independent and only zero maps to zero.