In each case, either show that the statement is true and include an example or give an example showing that it
If A is m × n and m < n, then Ax = b has a
solution for every column b. (Are we talking about rank here?)
If Ax = b has a solution for some column b,
then it has a solution for every column b.
i. If x1 and x2 are solutions to Ax = b, then x1
− x2 is a solution to Ax = 0.
Please provide full reasoning.