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The equations xy+2z=4,  3x+y+4z=6,  x+y+z=1have 

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a
unique solutions
b
infinitely many solutions
c
no solution
d
Two solutions

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detailed solution

Correct option is B

Δ=1-12314111=1(1−4)+1(3−4)+2(3−1)=3−1+4=0Δ1=4-12614111=41-4+16-4+26-1=-12+2+10=0 Δ2=142364111=16-4-43-4+23-6=2+4-6=0 Δ3=1-14316111=11-6+13-6+43-1=-5-3+8=0 ∴Δ=Δ1=Δ2=Δ3=0 ⇒the given system has infinitely many solutions


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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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