Subset and subspaces Determine whether the given subset H of the vector space V
ID: 2963214 • Letter: S
Question
Subset and subspaces
Determine whether the given subset H of the vector space V is a subspace of V. Justify your answers. V= C(-infinity, infinity); H={ f(x) | f(x) 0 } V= C(-infinity, infinity); H={ f(x) | f(-x) = f(x)} V= C (-infinity, infinity); H= {f(x) | f(x) = C } V= Mn times n ; H={ D Mn Time sn | D is diagonal} V= Mn times n ; H={T Mn times n | T is upper triangular } V= Mn times n ; H=( A Mn times n | A is invertible ) V= RLambda3 ; H = {(a,b,a+2b) a,b R} V= C [a,b]; H= {f C| f(x) dx= 0 } Prove : if U and W are subspaces of a vector space v, then U W is a subspace of V. Provide a counterexample to the false proposition that the union of two subspaces of a vector space is a subspace of the vector space. For what value(s) of alpha will the vectors (1,2,3), (2,-1,4), (3,a,4) be linearly dependent?Explanation / Answer
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