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

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

Document Summary

For which values of b is the matrix a = (cid:20)1. 1 (a) for any number b di erent from 0. (b) for any number b. (c) for b = 0. (d) for no values for b. (e) for any number b di erent from 1 and -1. The matrix a is invertible if and only if b b = 2b is di erent from 0, that means, b must be a number di erent from 0. Find an explicit description of the null space of. 0 0 0 that is, nd a minimal set of vectors v1, . , v p such that nul(a) = span{v1, . Nul(a) is the set of all solutions to the homogeneous equation. We identify x1, x2 and x4 as pivot variables and x3 as the free variable. Thus we can write the general solution as x1 x2 x3 x4.