Please give an specific example of each part. For example in part a, what is an example of a matrix that forms a linearly dependent set with a rank of 2 and a nullity of 3

1. For each case, give an example of a matrix with the stated properties OR explain why it is impossible to nd such a matrix. (a) B is a 4 x 5 matrix with rank=2 and nullity=3. Solution: This is possible. Any 4 x 5 matrix whose columns form a linearly dependent set, and whose columns can be culled to a linearly independent set of exactly two vectors will work. If it is not 100% obvious from your matrix, you must show extra work to justify why your matrix is valid. (b) C is a 4 X 5 matrix with rank=5 and nullity=0. Solution: This is impossible. The domain is R4, so it is impossible to have a linearly inde pendent set of ve vectors. Therefore, the basis for the column space cannot have ve vectors, so the dimension cannot be 5. (c) D is a 4 X 5 matrix with rank=3 and nullity=l. Solution: This is impossible because the ranknullity theorem fails. You should show this