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Question

# The number of 3×3 metrices A whose entries are either 0 or 1 and for which the system A=⎡⎢⎣xyz⎤⎥⎦=⎡⎢⎣100⎤⎥⎦ has exactly two distinct solution is?

A
0
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B
291
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C
168
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D
2
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Solution

## The correct option is A 0Let A=⎡⎢⎣a1b1c1a2b2c3a3b3c3⎤⎥⎦where ai,bi and ci have values 0 or 1for i=1,2,3Then, the given system is equivalent toa1x+b1y+c1z=1a2x+b2y+c2z=0a3x+b3y+c3z=0which represent three distinct planes. But three planes cannot intersect at two distinct points, therefore no such system exists.Hence, the correct answer.

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