Let X={a,b,c} and B={{a,c},{a},{b}}. Let T be the topology generated by B and consider A={a,b}. With respect to T, compute the closure A¯¯¯ of A and the boundary ∂A=A¯¯∩(X∖A)¯¯ of A. Let T be the topology generated by B and consider B={a,c} viewed as a subspace of X. Is there a set that is closed relative to B that is not closed in X? Justify your answer.

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Q: Let W be a subspace of a vector space V. Show that if x is in both W and W+, then x = 0.

A: Solution is given below

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.