1. The problem statement, all variables and given/known data Find all possible values of rank(A) as a varies. A=[1, 2, a] [-2, 4a, 2] [a, -2, 1] A is 3x3, just merge the 3 row vectors. 3. The attempt at a solution I have the solution but I create this thread to find the most effective/efficient procedure for me to solve these kinds of problems. What are the possible dimensions of the row/column space as a varies? When do the columns/ranks become linearly dependent based on different values for a? I don't want to guess or plug in arbitrary numbers; I want a generalized, systematic approach that works every time.