Label the following statements as true or false.(a) The zero vector is a linear combination of any nonempty set ofvectors.(b) The span of ᴓ is ᴓ. (c) If Sis a subset of a vector space V, then span (S) equals the intersection of all subspaces of V that contain S. (d) In solving a system of linear equations, it is permissible to multiplyan equation by any constant.(e) In solving a system of linear equations, it is permissible to add anymultiple of one equation to another.(f) Every system of linear equations has a solution.

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A: The empty subset of any vector space V is not a subspace of V The given statement is false.

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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.