Q. Are the vectors linearly independent? (Your answer to this question needs to

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Q. Are the vectors linearly independent? (Your answer to this question needs to start with the definition of linear independence. not with a matrix.) a. Let the set S={v1,v2,?.,vn} be a linearly independent subset of a vector space V. You are standing at the origin of V and set off in the direction of v1. After a certain length of time, you stop and head in the direction of v2 - then in direction v3, and so On. Is it possible for you to return to the origin? 1. Express, if possible, -9-7x-15x^2 as a linear combination of p1 = 2+x +4x^2, p2 =1-x+ 3x^2. 2. This question investigates overloading the operators in vector spaces, that is, redefining the + and scalar multiplication operations. ( a Suppse we consider R2, but where (a,b)+(c,d)= (a +c+1, +d + 1). Which, if any, of the 10 axioms of vector spaces are not met? (b) Consider the set of positive real numbers, with the following redefinition of + and .: What is the 0 vector? What is -3? Using the axioms of a vector space, show that each element has precisely 1 inverse.

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