MATH136 Lecture Notes - Lecture 5: Linear Combination, Linear Independence, Selenium

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Andre

Document Summary

Friday, may 5 lecture 3 : linear independence in n. (refers to sections 1. 3: linearly independent subset in n. Let m = {v1, v2, , vk } be k vectors in n and suppose the vector 0 represents the zero vector 0 = (0, 0, , 0). The solution where all the i s are zeros is called the trivial solution of this vector equation. If v1, v2, , vk are not linearly independent then they are said to be linearly dependent. Note that a linearly independent set cannot contain the zero-vector, 0. In class, we will often abbreviate the words linearly independent with the letters li . 3. 2 example verify whether the set {v1, v2, v3} in 3 where v1 = (1, 1, 1), v2 = (0, 1, 7) and v3 = (0, 0, 3) is linearly independent. 3. 3 theorem a non-empty subset of a finite linearly independent subset of m is linearly independent.