NOTE:  We do NOT calculate determinants using "minors" or "cofactor expansions" as might be demonstrated in other courses.
(That is a VERY inefficient way to compute a determinant.)
Instead, we learned how to calculate determinants efficiently using Gauss elimination.

1. Given the matrix:

   A   =   11 8 14 –5 55 49 77 –21 –33 84 45 71 88 127 155 –15

   1. Calculate det(A) using Gauss elimination as presented in class.   Answer:   det(A) = 3,861
   2. Would the system Ax = b have a unique solution?
   3. Would the system Ax = 0 have a unique solution?

2. Read and do the Maple example for calculating a determinant of a matrix. Use this to check your answer in Problem 1(a).

3. Suppose we have a system Ax = b, where b ≠ 0.
   1. What can be said about the number of solutions of the system if det(A) = 0?
   2. What can be said about the number of solutions of the system if det(A) ≠ 0?

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