12-240/Classnotes for Tuesday October 2
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The "vitamins" slide we viewed today is here.
Today, the professor introduces more about subspace, linear combination, and related subjects.
Subspace
Remind about the theorem of subspace: a non-empty subset W ⊂ V is a subspace iff is is closed under the operations of V and contain 0 of V
Proof:
First direction:
if a non-empty subset W ⊂ V is a subspace , then W is a vector space over the operations of V .
=> + W is closed under the operations of V.
+ W has a unique identity of addition: a W: 0 + a = a
Moreover, a a V. Hence 0 is also identity of addtition of V
Second direction
if a non-empty subset W ⊂ V is closed under the operations of V
we need to prove that
Class Notes
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