MATH 2211 Quiz: Quiz7mt210SPR11Ans

• School: Boston College
• Department: Mathematics
• Course: MATH 2211
• Professor: All

Document Summary

Let t : r3 r3 be the linear transformation de ned by (x1, x2, x3) 7 (x1 + x2 + x3, x2 + x3, x3). If it is, nd the formula for (t s) 1. Answer (a) the standard matrices a and b of t and s, respectively, are. Note that a i3 3 and b i3 3. Therefore, both a and b are invertible which means that s t and t s are invertible. By using the algorithm for inverse matrices, we calculate the inverses as and b 1 = . The standard matrix of (s t) 1 = t 1 s 1 is given by the multiplication. Thus, the formula for (s t) 1 is obtained as (s t) 1(x) = . We get (s t) 1(x) = (x1 2x2 + x3, 2x1 + x2, x1). (b) similarly, the standard matrix of (t s) 1 = s 1 t 1 is given by the multiplication b 1a 1.