Let V be a vector space over R, and let Sị and S2 be subspaces of V. (a) Prove that Si C S2 = dim(S1) < dim(S2). (b) Prove that (Sı C S2 and dim(S1) = dim(S2)) → S1 = S2. (c) Prove that if u1,..., uk are linearly independent vectors in V, and v E V with v 4 span(u1,..., Uk), then u1, ..., Uk, v are linearly independent. %3D

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A: 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.