4. Let B = {V1, V2, Vn} be a basis of a vector space, V. ... a) Prove just ONE of the following: • If S = Um} spans V then m > n. Um} is linearly independent then m < n. {u1, u2, ..., • If S = {u1, u2, b) Use (a) to show that the definition of dimension of V is well defined: That is, if B1 = {v1 , v2 , ..., Vn} and B2 = {u1, u2, ..., Um} are bases of V then m = n. %3D %3D

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Q: 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

A: Solution

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A: Note: according to our guidelines we can answer only 11 th question

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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.