MATH 415 Study Guide - Final Guide: Row And Column Spaces, Linear Map, Altgeld Hall

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

Document Summary

Computations: let t : r2 r2 be a linear transformation whose matrix with respect to the standard basis is. Let b be the basis consisting of the eigenvectors of te e . 2 (1) find is b (2) find the change of basis matrices ibe, and ie b. (3) what is the matrix tbb. 1/ 2(cid:21) ,(cid:20) 1/ 2: consider the two non-standard bases of r2, b = (cid:26)(cid:20)1/ 2. , v3: find all vectors in r3 which are orthogonal to both for these vectors. , v4 : let a = . Tutoring room (343 altgeld hall): monday 4-8pm, tuesday 6-8pm, wednesday 5-7, thursday 4-6. Piazza: https://piazza. com/class/j65464jkd255s: find a matrix whose row space contains such matrix exist. Testing your understanding: find examples for the following or say why they do not exists: (1) two vectors u, v in r3 such that u v = 13. 0(cid:21) and (cid:20)0 (2) a vector that is orthogonal to (cid:20)1.