4. Let B- (v, Va. Vn) be a basis of a vector space, V. a) Prove just ONE of the following: • If S- {u, ua, Um) pans V then m 2n. • If S- (ui. ua, .. Um) is linearly independent then m Sn. b) Use (a) to show that the definition of dimension of V is well defined: That is, if B = {V1, Va, Va) and B (u1, u2, , um) are bases of V then m = n.

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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.