Let A be a 4x4 matrix and Ax = b such that x = (x1, x2, x3, x4) and b = (b1, b2, b3, b4).
For each i let us mark the i-column of A with ai.
It is given that b = a2 + 2a3 + 3a4.
(1) Prove, using Cramer's rule or any other way, that if det(A) does not equal zero then the linear system has one solution in which x1 = 0.
(2) Is it true that there is a solution to the linear system in which x1 = 0 also when det(A) = 0? Prove or refute.
I already solved (1), but have no idea how to prove (2). Any suggestions?