Are the following statements true or false?

? True False  1. Let $m<n$. Then $U =$ {$u_1, u_2,\ldots, u_m$} in $R^n$ can form a basis for $R^n$ if the correct $n-m$ vectors are added to $U$.

? True False  2. Let $m>n$. Then $U =$ {$u_1, u_2,\ldots, u_m$} in $R^n$ can form a basis for $R^n$ if the correct $m-n$ vectors are removed from $U$.

? True False  3. The set {0} forms a basis for the zero subspace.

? True False  4. $R^n$ has exactly one subspace of dimension $m$ for each of $m = 0,1,2,\ldots, n$ .

? True False  5. The nullity of a matrix A is the same as the dimension of the subspace spanned be the columns of A.