MATH 271 Final: MATH 271 Amherst F13M271 2802Daniels 29Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 271
• Professor: All

Document Summary

Final exam: true or false: (no justi cation necessary) (a) If a and b are n n matrices such that ab is the zero matrix, then a is the zero matrix or b is the zero matrix. (b) If a is an n n symmetric matrix then a is invertible. (c) Any two orthogonal vectors are linearly independent. (d) (e) If a is an invertible matrix then = 0 is an eigenvalue of a. If w is a subspace of rn, then dim w = n dim w . , b = and let w = span{a1, a2, a3}. 775 the techniques learned this semester to determine if b is in w . Find the dimension of ker (t ). (c) Find the dimension of range (t ): let a = 2. Use a 1 to nd the solution to ax = 2. Find an invertible matrix c and diagonal matrix d such that d = c 1ac.