Question 985516
[0 0 0 5] means we have 0x+0y+0z = 5. The zeros are the coefficients to x,y,z


But there are no solutions to 0x+0y+0z = 5 because it becomes 0+0+0=5 which becomes 0 = 5. It's always false. There are no solutions. This system is inconsistent.



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[0 0 0 0] means 0x+0y+0z = 0 which ultimately leads to 0 = 0. It's always true, so there are solutions, and this system is consistent and dependent.