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Question

The number of 3×3 matrices A whose entries are either 0 or 1 and for which the system Axyz=100 has exactly two distinct solutions, is

A
291
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B
2
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C
168
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D
0
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Solution

The correct option is D 0
The equation Axyz=100has two distinct solutions. It should be noted here that the given equation is linear equation in 3 variables, which may have no solution, or unique solution or infinitely many solutions.
Hence there does not exist any matrix A such that the given equation has exactly two solutions and consequently number of 3×3 matrices is 0.

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