MATH115 Lecture Notes - Lecture 30: Aomedia Video 1, Orthogonalization, Linear Combination

• School: University of Waterloo
• Department: Mathematics
• Course: MATH115
• Professor: Tina Davidson

Document Summary

Tuesday, november 11 lecture 30: gram-schmidt orthogonalization process. Expectations: apply the gram-schmidt orthogonalization process linearly independent. So any linearly independent set can be expanded, one vector at a. Suppose w1 is not in span{v1, v2, ,vm}, and 1w1 + 1v1 + 2v2 + 3v3 + + mvm= Note that w1 cannot be the zero vector. Then 1 is 0 otherwise w1 would be a linear combination of the others and so would be in the span{v1, v2, ,vm}. Since 0w1 + 1v1 + 2v2 + 3v3 + + mvm= 0 forces the i"s to be zeros then. B1 ={v1, v2, ,vm , w1} is linearly independent. {v1, v2, ,vm , w1} to a larger linearly independent set by picking a vector outside of span{v1, v2, ,vm , w1}. 30. 1. 1 example we easily see that the set b = {(1, 2, 1), ( 1, 2, 1)} is linearly.