SUPERFANS OF MATHEMATICS

Theoram 5.2.8 state that:

If u1,u2,u3...uk are linearly dependent vectors in Rn  , then any superset of  {u1,u2,u3...uk} are linearly dependent....

huh? wat is superset? o.0
wikipediaING....

Theoram 5.2.10 state that:
Let U = {u1,u2,u3...uk} be a linearly dependent set of Rn. Then there exists a subset S such that
i) S is linearly independent
ii) S U (v) linearly dependent for any vector v in U but not S....

the superset of the dependent MUST b dependent....but dependent set still can form a subset which is independent, and it will change to dependent if add one of the vector from U to S....



ohyeah...
tats wat the BEAUTY of mathematics....

TRY MY BEST TO LOVE IT....
I WILL BECOME A SUPERFANS OF MATHEMATICS VERY SOON ...=)