Linearly independent (MAtrix)

The rows of the matrix:
Show it is linearly independent
1 4 2 3
2 2 1 1
3 1 2 11
I have the solution, but I don't understand.
Solution:
a(1 4 2 3) + b(2 2 1 1 ) + c(3 1 2 11) = (0 0 0 0)
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why the above equation can change to the below equations??????
a + 2b + 3c = 0
4a  2b + c = 0
2a + b + 2 c = 0
3a + b + 11c = 0
a=b=c=0, so it is linearly independent.
Confused