Hello everyone, I was wondering what the easiest approach would be to do this: Find values of k for which the matrix system Ax = b, has a) no solutions, b) infintie solutions, and c) a unique solution: A = 1 1 2 1 2 -3 7 17 k b = 1 -3 32 I remeber doing a homework problem that said, Find the value of k for which the matrix A had rank 2, it also had a k in it, but it was a 3x3 matrix, this one has a vector b, so i don't know what to do with that, or if i can ignore it. With my old homework problem, I found the value of k which would make the matrix A rank 2, by finding the determinant of the matrix and setting it equal to 0, then solving for k and it worked! But really what did i find? Did i find a case in which the system had no solutions by doing that? because if its rank 2, and its a 3x3, then it should be a rank 3 if it had a unqiue solution right? Sorry i'm getting off the subject of my orngial question but i think it might help me solve this also. But my real question i need help with is my first question above! thanks!