MATH 415 Study Guide - Final Guide: Scalar Multiplication, Elementary Matrix, Linear Combination

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

Document Summary

Multiple choice questions: mark answers on the scantron form. Make sure to enter your netid on the scantron! Also circle your answer on this exam booklet! Let a = (cid:2)a1 a2(cid:3) be a 2 2 matrix with columns a1 and a2. Which of the following two statements are true? (s1:) if a(cid:20)3 (s2:) if ax = (cid:20)3. 1(cid:21) = 0, then 3a1 + a2 = 0 is a dependence relation for the columns of a. So if a(cid:20)3 dependence relation for the columns of a. On the other hand, ax = (cid:20)3 that (cid:20)3. 1(cid:21) is a linear combination of the columns of a, so it is in col(a). 1(cid:21) = 0, then 3a1 + a2 = 0 is a. Let a = (cid:20) (s1:) if ax = (cid:20)1 (s2:) if a(cid:20)1. (cid:21) be a 2 2 matrix. 3(cid:21) = b for some vector b, then (cid:20)1.