MATH 415 Study Guide - Final Guide: Null Character, Altgeld Hall, Linear Map

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

Document Summary

Computations: find a basis for n ul(a), col(a), col(at ), and n ul(at ), for. In order to determine bases for the 4 fundamental subspaces, we rst bring a to echelon form: To obtain a basis for the null space, we need to get the relation between the variables. It is clear from the echelon form of a that x5 = 0, x3 = 2x4, and x1 = 2x2 2x4. Finally we need to nd a basis for n ul(at ) if we rst transpose. Tutoring room (343 altgeld hall): monday 4-8pm, tuesday 6-8pm, wednesday 5-7, thursday 4-6. The echelon form of a has pivots on columns 1, 3 and 5. The row space of a (i. e. col(at )) remains unchanged under row opera- Here, rows 1, 2, and 3 have pivots. 7 and then reduce we see that the echelon form of at is.