Consider the following matrix.

A =11235823c

a) Given Ax=b, apply the Gauss Elimination method to the augmented matrix. (b is a 3 by 1 vector.)

b) Take c=3. Find a condition on vector b which makes the system consistent. Then find a solution.

c) Now consider c as a variable (not necessarily 3). Form the vector b with last 3 digits of your student number. (If last 3 digits of your student number are b1b2b3, the first entry of vector b is b1, the second entry is b2, the third entry is b3.) Determine (if possible) the value of c for which the matrix system has a unique solution, no solutions, and infinitely many solutions. Explain.