(5 points) Defining the a1, a2,...,an being n column vectors in, R2 and let A = [a1 a2 ... an],(1)the vectors a1,a2,..., an will be linearly independent if and only if A is nonsingular.
(2) the detcrminate of A is nonzero.
(3) the vectors a1, a2, an will be linearly independent if and only if the null space N(A) ={0}.
(4) the rank of A plus the nullity of A equals n.
(5) the rank of ATequals the rank of A.