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Which of the following matrices can NOT be obtained from the matrix [ -1 2 ; 1 -1 ] by a single elementary row operation ?

1. [ 0 1 ; 1 -1 ]
2. [ 1 -1 ; -1 2 ]
3. [ -1 2 ; -2 7 ]
4. [ -1 2 ; -1 3 ]

Correct answer: [ -1 2 ; -2 7 ]

Solution

The matrix [ -1 2 ; -2 7 ] cannot be obtained from the original matrix through a single elementary row operation because it requires changing both elements of the second row, which is not possible with just one operation that affects only one row or swaps rows.

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