Solutions of Linear Systems III

Write a short paragraph to answer each of the following questions about solutions of systems of linear equations. You should not perform any calculations, but instead base your explanations on the appropriate properties.

[5] The linear systems Ax = b1 + b2 necessarily consistent? Why or why not?

[6] Consider the linear system Ax = b. If the rank of A equals the rank of the augmented matrix for the system, explain why the system must be consistent. Contrast this to the case in which the rank of A is less than the rank of the augmented matrix.