Need help on 6-12

6 Let A be a 2 x 2 matrix with rank(A) = 1. What is dim(Nul(A))? (7) Write down three 2 x 2 matrices with rank 1. (8) For each of the three matrices A you chose in problem 7, graph Nul(A) and Row(A) on the same axes. What is the relationship between these two subspaces? (9) Is every subspace of R" equal to Col(A) for some matrix A? Why/why not? For problems 10-12: is a matrix with the following properties possible? If yes, give an example; if not, explain why. (10) A 3 x 4 matrix A with Col(A) = 3. (11) A 2 x 4 matrix whose columns are linearly independent. (12) A 4 x 2 matrix of rank 3