anonymous
  • anonymous
why we ignore the last row of augmented matrix if it consists entirely of zeros?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1327674600709:dw| isnt the last row be 0x+0y+0z=0 and have infinitely many solutions.
amistre64
  • amistre64
who says we ignore it?
amistre64
  • amistre64
the last row tells us the when 0=0 we have that many solutions; well, 0 always = 0 so there are infinitely many solution

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amistre64
  • amistre64
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
  • amistre64
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
  • anonymous
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?

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