why we ignore the last row of augmented matrix if it consists entirely of zeros?

Question

anonymous · Answer

|dw:1327674600709:dw|
isnt the last row be 0x+0y+0z=0
and have infinitely many solutions.

amistre64 · Answer

who says we ignore it?

amistre64 · Answer

the last row tells us the when 0=0 we have that many solutions; well, 0 always = 0 so there are infinitely many solution

amistre64 · Answer

it also tells us that the last row doesnt add any new information to the system.  deleting that row would still give us the right answers

amistre64 · Answer

1x+3y = 5
-2x + y = 7
  4x -2y = -14

for example


since eq3 is just a multiple of eq2 then it doesnt give us any new information to help solve the system does it?

anonymous · Answer

in other words we can say that the solution of 1st two equations will also satisfy the 3rd equ but any solution of 3rd equ will never satisfy the 1st two equations so we ignore the 3rd row right?