B02. 136.130: Test #2 Solutions

1. Find the inverse of each of the following two matrices, or show it does not exist.

, .

Solution.

For A: after row reducing becomes ; so the inverse of A is .

For B: after row reducing becomes (some entries * to the right); So, B is not invertible.

2. You are given that the inverse of is . Solve the following system using the method of inverses (no marks if other methods are used).

Solution. The only solution is .

3. Compute the determinants of the following matrices (there are shortcuts for the last two matrices):

,    ,    ,  

Solution. , , (because of the 0-column) and (product of the entries in the main diagonal).