Prove the following infinite-dimensional version of Theorem 1.7: Let ß be a subset of an infinite-dimensional vector space V. Then ß is a basis for V if and only.if, for each nonzero vector y in V, there exist unique vectors X1, ...,Xn in ß and unique nonzero scalars C1,...,Cn such that y = C1X1 +...+ CnXn

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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.