I've stumbled upon this question, and I have to say that I'm completely lost. I have no idea how one can find the amount of solutions of the system Ax = 0 when this is the case:
Let A be a 3 × 3 matrix and suppose that 2a_1 + a_2 − 4a_3 = 0.
(a) How many solutions will the system Ax = 0 have? Explain.
I also do not know how to answer this question, I know that a matrix is nonsingular when for a certain n x n matrix A, there exists a matrix A^-1 such that A * A^-1 = I_n
(b) Is A nonsingular? Explain.
Thanks in advance.