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Solution

solutiion:\'

if the given system of equations have exact one solution then the equations are said to be independent

otherwise in all cases means no solution or infinite solution or more than one solution

these are said to be dependent

now without solving inverse matrices we can just solve for three unkowns from three equations

if only one solution comes then independent otherwise dependent+

now

-3z=6

2x+y-2z=6

-6x-3y=-6

on solving these two equations become same

hence ininite solutions hence consistent