Which of the following cases will not lead to non trivial solutions in case of system of linear equations according to Cramer's rule Convention given D != 0 ?

D1 = 0, D2 = 0, D3 = 0

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D1 = 0, D2 = 0, D3 != 0

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D1 != 0, D2 != 0, D3 = 0

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D1 != 0, D2 != 0, D3 != 0

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Solution

The correct option is A
D1 = 0, D2 = 0, D3 = 0

1) D != 0, at least one of D1,D2,D3 != 0

Then there exists a non trivial solution implies nontrivial solution possible

2) D ! = 0, D1 = D2 = D3 = 0,

only the trivial solution exists implies nontrivial solutions are impossible

From case 1 and 2 non trivial solutions are possible only if at least one of D1,D2,D3 != 0. So option a is correct.

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