Question

R² R3 Where M (72 = 147 where Consider the Linear map : cosa-sing o A = [998 cool ] show that A is an matrix orthogonal Decribe geometrically how the maps M and Mr more vetons in R"

Answer 1

There are two way to prons it. i) we know that A square mamin 'Als Orthogonal if AATE ATA :) OR i) Sum of square of eeich element of equal to 1 and product of one now to di'shnut each how you is 0 COMO using in • sind AAT coso + Sino It Sino coso -Sino TO - 0 Cabot sinho -LT o 0 O 0-Sind con o- lad Sind Sino? Sino como sino tamo TA O o using ii) colo t sinh to = corrotsblo=1 Sinto to colo to 0² - Sinto tcoils=1 2 to2 +1 Oto +171 & -Sino coro it cow sino to- 0 + 0+ o toto Therefore, ginen ginen marin is orthogonal. Again AT-A1 coso Sino -Sind cono :] 0

e₃ Sinbo + coche to2 =1 Coire + sinke to =1 0²602612 21 for 'M a e 2 Cow te, + sinho to²=1 Sino + coilo toal 02+02 +12 for Mt. =1 Both have identical geome memical Interbritan'or.