MATH 417 Midterm: MATH417 Midterm 2 2017 Spring with Solution

• School: University of Illinois
• Department: Mathematics
• Course: MATH 417
• Professor: All

Document Summary

Math 417 spring 2017 section b1. Solutions: (25 points) let m2(r) be the ring of real 2 2-matrices. Con- sider the subset b m2(r) given by: (cid:26)(cid:18) a b b a (cid:19) Which of the following statements are true/false (justify! (a) b is a subring of m2(r); (b) b is an ideal of m2(r); (c) b has no zero divisors. The di erence and the product of two matrices in. B is a matrix in b: (cid:18) a1 (cid:18) a1 b1. B1 a1 (cid:19) (cid:18) a2 (cid:19)(cid:18) a2 b2. B2 a2 where a = a1 a2 and b = b1 b2. (cid:19) (cid:19) (cid:19) (cid:18) a b b a (cid:19) (cid:18) a b b a b1. B2 a2 where a = a1a2 b1b2 and b = a1b2 + a2b1. (b) false. The product of a matrix in m2(r) by a matrix in. B may fail to be in b, for example i b but: (cid:54) b.