If a linear system is inconsistent, what can we conclude about its linear independence?

Question

anonymous · Answer

Linear systems will be mutually exclusively either inconsistent, dependent, or independent.  Since the system is inconsistent, it cannot also be independent.

anonymous · Answer

|dw:1355976616595:dw|So it will be like this: it fits into only one of the three and only one .

anonymous · Answer

All good now?

anonymous · Answer

yes thank you!

anonymous · Answer

BTW,  inconsistent lines are parallel, dependent lines are the same line, and independent lines intersect.  That's why it can be only one case at a time.

anonymous · Answer

And thx!  Nice working with you and good luck in your studies!

anonymous · Answer

thats a good way of looking at it.

anonymous · Answer

wait in R2, 1 0 and 0 1 are independent but it can never intersect

anonymous · Answer

but a linear combination can make it intersect with either vector. ok im answering my own questions now. lol