Let A = , b = Find all vectors x R3 such that Ax = 0 Recall that 0 is the zero vector whose entries are all zeroes. Find all vectors x R3 such that Ax = b Denote by ker(A) = {x R3|Ax = 0}. Show that if x, y ker(A), and alpha R, then x + y ker(A), and alpha x ker(A). The set ker(A) is called the kernel of the matrix A. The set of vectors b such that Ax = b for some x is called the image of A.