(5 points) Defining the a
1, a
2,...，a
n being n column vectors in, R
2 and let A = [a
1 a
2 ... 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.
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