(5 points) Defining the a₁, a₂,...，a_n  being n column vectors in, R² and let A = [a₁ a₂ ... an],

(1)the vectors a1，a2，...， a_n will be linearly independent if and only if A is nonsingular. 

(2) the detcrminate of A is nonzero.

 (3) the vectors a₁, a₂,  a_n 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 A^Tequals the rank of A.

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