MATH 21 Study Guide - Final Guide: Orthogonal Complement, Symmetric Matrix, Pythagorean Theorem
Document Summary
Math 21 practice problems for final fall 2016. 3-4 problems from chapters 2 and 3 ( 2. 1 2. 3, 2. 7 2. 9, 3. 1 3. 2), and 6-8 problems from. Some problems will overlap various chapters, e. g. part (b) of the rst question below draws from chapter 6. Chapter 1 (a) de ne what it means for a set of vectors {v1, . , vk} in rn to be linearly inde- 1. pendent. (b) show that if {v1, . , vk} is an orthogonal set of nonzero vectors, then the vectors: is the vector. 1 using methods from chapters 1 and 2. ) (note: this is really: are the vectors. 1: write down the matrix for the linear transformation t : r2 r2 that scales by a factor of 3 and rotates counterclockwise by an angle of 45 degrees. Chapters 2 3 (a) de ne what it means for a subset h rn to be a subspace. (b) de ne span(v1, v2, .
