1) If the linear transformation T: R^n --> R^n is one-to-one and T(u-v) = 0, then u = v (u and v being vectors and 0 being the zero vector).
2) If the linear transformation R^n --> R^n is onto T(u-v)=0, then u=v (u and v being vectors and 0 being the zero vector).
3) If det(A) = 0, then T is neither onto nor one-to-one.
4) If T: R^n --> R^m is not one-to-one, then ker(T) contains infinitely many vectors.
5) Shears in R^2 are one-to-one linear operators.
2007-08-09
10:52:45
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2 answers
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asked by
Anonymous