MATH 415 Study Guide - Final Guide: Row And Column Spaces, Free Variables And Bound Variables, Matrix Equivalence

• School: University of Illinois
• Department: Mathematics
• Course: MATH 415
• Professor: J Li

Document Summary

Question library question correct answer your answer points. Let v be a vector space that is spanned by three linearly independent vectors v1, v2, v3. Which of the following vectors form a basis of v ? (a) v1, v1 + v2 + v3, v2 + v3. (b) none of the other answers. (c) v1, v2, v2 v1. (d) v1, v2 v1, v3. We know already from the statement of the question that {v1, v2, v3} is a basis of v and so dim (v ) = 3. Thus, we are looking for a set of three linearly independent vectors spanning v . Among the given choices only {v1, v2 v1, v3} satis es these properties. Indeed, the vector v1 v2 is a linear combination of v1 and v2, and v1 + v2 + v3 is a linear combination of v1 and v2 + v3. Let denote the standard inner product in rn.