MATH 415 Study Guide - Final Guide: Lu Decomposition, Identity Matrix, Invertible Matrix

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

Document Summary

Computations: for the following matrices a and b, nd an elementary matrix e such that ea = b. From the corresponding elementary row operations we obtain that: 1 1 1: suppose a is a matrix with rows a = . Express the rows of b in terms of the rows of a. E1 is the elementary matrix corresponding to the operation r3 r3 + 2r2, and e2 is the elementary matrix corresponding to r1 r3. Tutoring room (343 altgeld hall): monday 4-8pm, tuesday 6-8pm, wednesday 5-7, thursday 4-6. R3 + 2r2: let a = . Therefore the appropriate elementary matrices are e1 = . 0 1 0: find an lu factorization for the following matrices. (1) (cid:20) 2 (2) (3) . Solution. (1) we take our matrix to ref and keep track of the corresponding elementary matrices: Using the above ref as u and e 1. 1 as l, we get the following lu decomposition: