The probability that it will rain tomorrow is. The probability that our team will win tomorrow's
1 answer:
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Answer with Step-by-step explanation:
Suppose T is one-one
Let S be a linearly independent subset of V
We want to show that T(S) is linearly independent.
Suppose T(S) is linearly dependent.
Then there exist and some not all zero scalars
such that
T is linear therefore,
T is one-one therefore
N(T)=0
S is linearly independent therefore,
It is contradiction.Hence, T(S) is linearly independent.
Conversely, Suppose that T carries linearly independent subset of V onto linearly independent subsets of W.
Assume that T(x)=0 if the set x is linearly independent
Then, by assumption we conclude that {0} is linearly independent but {0} is linearly dependent.
It is contradiction .Hence, the set {x} is linearly dependent which implies that x=0
It means N(T)={0}.Therefore, T is one- one