Let v1,v2,v3\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3v1,v2,v3 be three column vectors in R3\mathbb{R}^3R3, and let A=[v1∣v2∣v3]A = [\mathbf{v}_1 \mid \mathbf{v}_2 \mid \mathbf{v}_3]A=[v1∣v2∣v3]. Which statement is correct?
The vectors are linearly independent if and only if det(A)≠0\det(A) \neq 0det(A)=0
The vectors are linearly dependent if and only if det(A)≠0\det(A) \neq 0det(A)=0
If det(A)=0\det(A) = 0det(A)=0, the vectors definitely span R3\mathbb{R}^3R3
det(A)=0\det(A) = 0det(A)=0 implies at least one vector is the zero vector