MATH125 Lecture Notes - Lecture 4: Dot Product

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

Let u, v and w be vectors in rn and let c, d be scalars, i. e. real numbers. By property (b) of the theorem we may unambiguously write u + v + w without parentheses since we may group the sum- mands in whichever way we want. By (a), we may also rearrange the summands; for example as w + u + v. likewise, sums of four sum- mands or more vectors can be calculated without regard to order or grouping. , vk are vectors in rn we will write such sums without parentheses: v1 + v2 + + vk. Let a and b be vectors in rn. 3a + (5b 2a) + 2(b a) = 3a + 5b 2a + 2b 2a. = (5 + 2)b + (3 2 2)a. If 5x a = 2(a + 2x) solve for x in terms of a. Here a and x are vectors in rn.