The first three columns of a 3x7 matrix A are linearly independent. For each of the following statements about A, decide if that statement always holds.

(i) Yes/No...The null space of A has a non-zero element in it.

(ii) Yes/No...The rows of A are linear independent.

(iii) Yes/No...The equation Ax=bhas a solution for any 3x1 column vectorb.

(iv) Yes/No...Every vector in $\displaystyle R^7$ is a linear combination of the rows of A.

(v) Yes/No...The fourth column of A can always be written as a linear combination of the first three columns of A

(vi) Yes/No...The rank of $\displaystyle A^T$ is 3

I and very lost with this question. I missed a few days of class and this was the material that was covered. If there is anyone that would be able to answer these questions and give good explanations why, it would be greatly appreciated. Thanks in advance!!