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. |