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Solution to Problem10


*****

Problem10:

Which of the following are elementary matrices?

> (a);

                                   [ 1    0]
                                   [       ]
                                   [-5    1]
> (b);
                                 [0    0    1]
                                 [           ]
                                 [0    1    0]
                                 [           ]
                                 [1    0    0]
> (c);
                              [2    0    0    2]
                              [                ]
                              [0    1    0    0]
                              [                ]
                              [0    0    1    0]
                              [                ]
                              [0    0    0    1]


SOLUTION:


Let's call the matrices A, B and C. A is the matrix representation of the elementary row operation that adds (-5) times the first equation to the second equation. B is the matrix that performs the swapping between the first and third equations so it is also elementary. Now C is not an elementary matrix. The only way to get a 2 on the upper left corner with an elementary row operation is to multiply the first row of the identity by 2, but then the last column should be 0 and not 2.


Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Wed Feb 9 10:00:01 EST 2000