- #1
MarcL
- 170
- 2
I'm just having a small trouble understanding the difference ( occurred while I was doing exercise).
A basis is defined as
1)linearly independent
2)spans the space it is found in.
Here is where I get confused:
To determine whether or not a set spans a vector space, I was taught to find its determinant and if det|A|=/= 0 then it spans the space.
I was also taught that if det|a|=/=0 then it isn't coplanar and therefore it is linearly independent ( can also just solve to see if trivial sol'n...)
But then if both det|a=/= it means that it spans and is linearly independent. Therefore, in my head, it comes with the idea that "spans is related to independence"
Anybody got a good way to differentiate both?
A basis is defined as
1)linearly independent
2)spans the space it is found in.
Here is where I get confused:
To determine whether or not a set spans a vector space, I was taught to find its determinant and if det|A|=/= 0 then it spans the space.
I was also taught that if det|a|=/=0 then it isn't coplanar and therefore it is linearly independent ( can also just solve to see if trivial sol'n...)
But then if both det|a=/= it means that it spans and is linearly independent. Therefore, in my head, it comes with the idea that "spans is related to independence"
Anybody got a good way to differentiate both?