I understand that there must be a solution because (1,2,3) is linearly dependent these columns. However, if I look at it from a matrix perspective, the matrix is inconsistant, which means that there is no solution. Why is there a conflict?

(8 points) Let 1 1 A = 2 4 4 3 7 k (a) (3 points) Find all values of k for which the system Ar = (1, 2, 3) has no solutions (you do not need to solve the system). Solution: 1 1 1 2 4 0 2 2 187- 183. 2 4 4 k - 3 k - 7 0 3 7 k 3 There is no value for & that will allow this system to have no solution