12.13 Solutions to Matrix Test 1B

This test and the one with question one beginning with the name Heather are intended to be similar enough that you could use the tests in the same class if you do not want to give all the students the same test.

Note: The first name on this test is Gail.

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5. Augment the matrix with the identity matrix like this:
   
   
   
   

   Then perform Gauss-Jordan elimination on the augmented matrix. The inverse is
   

   
   
   

   Note that the students were only asked for the steps OR the inverse.
   

6. Answers will vary. Matrix is a generic 2 by 2 symmetric matrix. The matrix is symmetric because A = A^T.
   

7.  
   

   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.
   

8. 22
   

9. 1. Inconsistent because the last equation reduces to a contradictory equation. Note that the students could also have used the appearance of the last row for reason for their solutions.
      

   2. Consistent and uniquely determined because there is a single solution.