MATH 551 Midterm: MATH 551 KSU A Test2 s17

• School: Kansas State University
• Department: Mathematics
• Course: MATH 551
• Professor: All

Document Summary

Problem 1 [10 points] write the vector b as a linear combination of the vectors v1 and v2: v1 = (cid:20) 1. Problem 2 [10 points] determine whether the given set is a subspace in r2. If it"s not, list the conditions which are false: S = {(x1, x2) r2 | x1 x2 = 1}. Problem 4 [10 points] find an lu -factorization of the matrix a or explain why it does not exist: Problem 5 [10 points] draw the non oriented graph with adjacency matrix a. Using the graph, determine the coe cient c1,2 of [ci,j] = a3 and write down all corresponding walks. Problem 6 [10 points] find a basis and the dimension of the subspace s = span{v1, v2, v3, v4} of r3: v1 = . Problem 7 [10 points] find a basis and the dimension of the following subspace. U = (cid:8)(x1, x2, x3, x4) r4 | x1 x2 + x3 x4 = 0(cid:9) .