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

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

Document Summary

Computations: determine a basis for each of the following subspaces: 0 0 0 1 0 (ii) k = (i) h = (iii) col (iv) nul : let u1 = (cid:20)1 (i) let v = (cid:20)2 (ii) let w = (cid:20)1. Express v in terms of the basis b (i. e. , realize v as a linear combination. Express w in terms of the basis b. of the vectors from b). Testing your understanding: construct a matrix withe the required property, or explain why such a matrix cannot exist. , nullspace has basis (2) column space has basis . 3(cid:21), row space contains (cid:20)3 (4) left nullspace contains (cid:20)1. 1 (3) dimension of nullspace = 1 + dimension of left nullspace. 3 (5) row space = column space, nullspace 6= left nullspace: consider the vector space p2 of polynomials of degree at most 2. Let b = {t2+t+1, t+1, 1} and q(t) = t2 + 1.