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The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

1. 5
2. 6
3. at least 7
4. less than 4

Correct answer: at least 7

Solution

A 3 × 3 non-singular matrix with four entries as 1 and one entry as 0 must have a unique arrangement that maintains linear independence among its rows and columns. The configurations that satisfy this condition can be achieved through various placements of the 1s, leading to at least 7 valid matrices.

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