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 For the equations    x+2y+3z=1, 2x+y+3z=2, 5x+5y+9z=4

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a
There is only one solution
b
These exist Infinitely many solutions
c
There is no solution
d
None

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detailed solution

Correct option is A

Augmented matrix AD= 123121325594 R2→R2−2R1:R3→R3−5R1                                                        =12310−3−300−5−6−1     R3→3R3−5R2                                                         =12310−3−3000−3−3∴rankA=rankAD=3⇒The given system of equations has a unique solution


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The number of 3×3  matrices A  whose entries are either 0or1  and for which the system Axyz=100  has exactly two distinct solutions, is


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