Answer to Question #2403 in Linear Algebra for gurdeep
Consider the set of all functions [0,1] which are discontinuous. check if this set is a vector space over R with respect to pointwise addition and scalar multiplication
It is necessary to verify axioms of a vector space. The verification is direct. For instance, If f,g : [0,1]->R are two functions and T is a real number, then & f+g& and T*f are also a functions [0,1]->R.
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