1. Make up a system of two linear equations, with two variables, that has infinitely many solutions.
2. Make up a system of two linear equations, with two variables, that has no solution.
3. If the product of two numbers is zero, then one of the numbers must be zero. Make up two 2 × 2 matrices A and B such that AB is a matrix of all zeros, but neither A nor B is a matrix of all zeros.
4. Suppose that we try to solve the matrix equation AX = B by using an inverse matrix but find that even though the matrix A is a square matrix, it has no inverse. What can be said about the outcome from solving the associated system of linear equations by the Gauss-Jordan elimination method?