MATH 3A Final: MATH3A Final Exam 2015 Spring

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 3A
• Professor: All

Document Summary

Spring 2015 math 3a final exam practice problems: determine whether each of the following subsets of r2 is a subspace. 1 (cid:104) 1 (cid:105) (cid:104) 2 (cid:105) (b) let a = [ (cid:126)v1 (cid:126)v2 (cid:126)v3 ]. Is a invertible: let b =(cid:8)(cid:2) 1 2 (cid:3) , [ 3. 1 ], what is (cid:126)y (in standard coordinates)? (b) find [(cid:126)x]b, where (cid:126)x = [ 5. 1 (cid:126)v1 = (cid:126)v2 = (cid:105) (cid:104) 2. 4: find the dimensions of the column space and null space of each of the following matrices. For each null space or column space with dimension at least 1, nd a basis. (cid:105) (a) (cid:104) 1 2 0. 0 0 0 0 0 (cid:35) (c) (cid:34) 0 0 0 0 0. 5 (cid:126)v1 (cid:126)v2 (cid:126)v3 (cid:126)v4 (cid:126)v5 (cid:126)v3 (cid:126)v2 (cid:126)v1 (cid:126)v4 (cid:126)v5 (cid:126)v1 (cid:126)v2 3(cid:126)v4 (cid:126)v3 (cid:126)v4 (cid:126)v5 (cid:126)v1 (cid:126)v2 (cid:126)v4 (cid:126)v4 (cid:126)v5 (cid:126)v5 (cid:126)v3 (cid:126)v2 2(cid:126)v4 (cid:126)v1 (a) (b) (c) (d) (e: let a =