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    Discrete Math Proper Subsets

    Discrete Math "Proper Subsets" Hey everyone, I am confused on part of this. Any input would be much appreciated!! X has ten members. How many members does ~P(X) have? (~P is the set of all subsets) How many proper subsets does X have? Well the number of members of ~P is 2^10 or 1024...
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    Kernel, Range, Basis (linear algebra)

    Okay that makes sense. Thanks guys! The basis is the standard basis of {(1,0),(0,1)} And the range can be any number in R2. and yes the dim Ker(T) is 1, dim Range(T) is 2, dim Domain(T) is 3.
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    Kernel, Range, Basis (linear algebra)

    Sorry the transformation is T(x,y,z) = ( x + y, z) Any ideas what the basis is?
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    Kernel, Range, Basis (linear algebra)

    Hey all! I am working on this and got confused. Any help at all would be much appreciated! Determine the kernel and range of the transformation T and find a basis for each: T(x,y,z)=(x,y,z) from R3 to R2. I have found the kernel to be the set {(r, -r, 0)}. Range is R2. I"m not sure how...