MATH 3A Study Guide - Midterm Guide: Row Echelon Form

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 3A
• Professor: All

Document Summary

Monday october 19, 5:00- 5:50pm october 20, 2015. Exercise 1 (a) [8, 4, 3, 5]t . (b) [8, 4, 3, 5]t (same computation as (a)). (c) x4[1, 0, 1, 1]t + [0, 0, 1, 0]. (d) 0 (e) reduced row echelon form has zero row: columns do not span r4. Reduced row echelon form has free variables: columns not linearly independent. One has (4, 0) = t ((2, 0)) (cid:54)= 2t (1, 0) = 2(1, 0). (b) false, 3 vectors never span r4 (there will always be a zero row in the matrix with the vectors as columns. (c) true. If c1v1 + c2v2 + c3v3 = 0 with not all ci = 0, then one has c1v1 + c2v2 + c3v3 +v4c4 = 0.