Question

Find ATA and AAT. A = -1 1 0 2 24 (a) AA E (b) AAT Which of the products are symmetric? (Select all that apply.) SATA LAAT

Answer 1

Dute. / ben find ATA AIA and and AAT -1 ht 2 2 J 2 АТ 1 2 4 ex toy au ar2 We know know that 31 Aa f a21 922 272 then AT = au 921 atz 427 272 bil biz and if B = Dzi bizz 22 2.X2 then bil a12 1911 biz 12 A B = bzz azz 22 a21 þzi air bli + 912.921 an biz +912.322 921: bil + 9221621 a21 b12 +922322 5 Alone ot -/ 2 ALAT z 2 2 4 2 3x20

Date: 2 2. 이 1, A AT 2. 2 2 10 HT2) +1(2)+9 (-1)) + 7) + 0) 24) + 2 (0) +4lo) 2:2) +22) +44) -2 +2 + ㅣ커 40 TTTT -2 +2 +0. 4 + +16 2. - AAT 7 29 Hence 2. AAT = 24 271

Date: B # @ ATA I 2 07 2 2 2 4 393 342 (-1).0+ 2-4 (-1)(-1) + 2 (2) (1)(-1) + 2 (2) 0 (-1) + 4(2) (20)+22 (00 +2.2 1:0 + 2.4 olu+462) 060 +4:4 1 + 4 -1 + 4 ota -174 1+4 ota O +8 O+ 8 o ti6 APA 5 3 8 3 5 M Ꮻ 16 3x3 Ans Lay Symmetne matnya A square matrix is said to be metric A=AT symn if ie A = {air y symmetric et ail qi : Fu, i have fox q ATA

Dule: 5 3 ATA = 3 16 3x3 Since AT A is Square matrix and = نه aji fill for 912 3 = Aal 8 :ههه azt 432 a 23 Hence. ATA ci Sym metn.c. 2 = More for AAT To 24 of ais aji fij 9,2 = = 92, or ☆ let AAT = B then B v spoon. Syemne fire of BT = B AT 2 f 297 o Pence की AAT i symmetric matine. AAT & AT hoth are Symmetre matrix