MATH 415 Study Guide - Final Guide: Redox, Altgeld Hall, Deuterium

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

Document Summary

Computations: determine a basis for each of the following subspaces: : a 3b + c = 0 (ii) k = (i) h = (iii) col (iv) nul . Solution. (i): every vector in h is of the form where s, t range freely over r. thus. Since these two vectors are linearly independent (there are two of them and they are not multiples of each other), the set is a basis of h. 1 (ii) we observe that k = nul(a) where. Tutoring room (343 altgeld hall): monday 4-7pm, tuesday none , wednesday 5-7, thursday 4-6. Since a is already in rref, we see that a is the pivot variable and b, c, d are the free variables. Thus we get as the general solution to the homogeneous equation ax = 0, a b c d. 3b c b c d where b, c, d range freely over r. thus,