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Q.

The system of equations2x+6y+11=0,   6y−18z+1=0, 6x+20y−6z+3=0is

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a

consistent

b

has unique solution

c

inconsistent

d

cannot be determined

answer is C.

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Detailed Solution

We have, augmented matrix AD=260-1106-18-1620-6-3                                                                  R3→R3-3R1                                                              ~260-1106-18-102-630                                                                   R3→3R3-R1                                                               ~260-1106-18-100091 Here rank A=2 and rank AD=3 ⇒ rank A≠rank AD ⇒The given system of equations is inconsistent.
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The system of equations2x+6y+11=0,   6y−18z+1=0, 6x+20y−6z+3=0is