Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) If W is a subspace of a vector space V, then it has closure under scalar multiplication as defined in V.(b) If V and W are both subspaces of a vector space U, then the intersection of V and W is also a subspace.(c) If U, V, and W are vector spaces such that W is a subspace of V and U is a subspace of V, then W = U.

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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.