BSNS102 Study Guide - Final Guide: Linear Algebra, Hypotenuse, Australian Council Of Trade Unions

• School: University of Otago
• Department: Business Studies
• Course: BSNS102
• Professor: Drew Stelljes

Document Summary

For any set, the additive inverse of x, denoted by x, is the element that yields the additive identity of that set (zero) when added to x. Put simply: x + ( x) = 0. (again, despite the typeface used for the variables, we are talking about sets in general. ) In other words, elements in the set can be negated. The negation operation can be applied to vectors. Every vector v has an additive inverse v of the same dimension as v, such that v + ( v) = 0. (we will learn how to add vectors in section 5. 8. ) To negate a vector of any dimension, we simply negate each component of the vector. Applying this to the specific cases of 2d, 3d, and 4d vectors, we have: Negating a vector results in a vector of the same magnitude but opposite direction. Figure 5. 2: examples of vectors and their negatives.