12.14 Solutions to Matrix Test 1C

This is the test that begins with a question about Canine Cabins. This test is more abstract and more difficult than the other two tests. If your students are advanced, you might consider using this test. Otherwise, these problems can serve as good extra credit problems or enrichment problems. This test will also take longer to grade because many of the questions have answers that may vary, so you will have to check to make sure the students' answers are correct without the help of an answer key.

1. 1.   and
      

   2.  
      

   3.  
      

   4.  
      

   5.   where
      

   6.   where
      

   7. Money needed = Ordered * Complete * Cost = $3190
   
   

2. AB^TC, A^TC^TB, BA^TC^T, CAB^T, C^TBA^T, B^TCA
   

   
   

3. 1. det (A) = (-2 + 12 + 3) - (-3 + 12 + 2) = 2
      

   2.  
      

      Gauss-Jordan elimination uses elementary row operations until the matrix to the left of the bar is the identity matrix. Gaussian elimination uses elementary row operations until the matrix to the left of the bar is an upper triangular matrix. Then it uses back substitution to find the values of x.
      

   3.  
      

   4. Show that AA^-1 = A^-1A = I.
   
   

4. The answers may vary.
   

5. The answers may vary.