Question

Given -1 1 A= = 20 0 find elementary matrices E1, ..., Ex such that Ex---E, E, A = 13.

Answer 1

Elementary matrices : An nan matrix obtained by applying a single elementary row operation on In is said to be elementary matrix of order n. There are threre type of elementary matrices given by " the elementary matrix obtained by applying Ris on In (where Reja Ri+R;) by Fij al Bis (In) = Eijor Rij- Eis in the elementary matrix obtained by applying CRi on In (where where cria cx Ri) is densted by Eis in Chili)= Eifc) or cRizfice) (N) The elementary matrin obtained by applying Ris (c) on In (where Riy (C) = Ri+C R; ) is denoted by Bij (C) ve Rij (c) (In) = Eis (c). Or Ris (c) = Ei; (c) o o For example E2 32/6 o ),6,10=6:30) 6 с Fistes 0

- A 2. 3 let us apply elementary row operations on A to reduce it to Echelon matrix. a row reduced IR2 1/2 2 R₂-2R An R3-3R, 2 3 - 2 0 3 -2 Rp + R2 o /2 7-2R2 0 Y2 Rotters -V2 R, 1/2 R3 o O O R₂-3 R2 O -1/2 -V2 → 0 O 0 13 So We can write this system as, (8 + x)(8 ++ R) (-28)(R3-6)(R+R) (46)(-)(8.–2P)]A = Iz → E34) E23 (1) 5 (-2) E32(3) Eq0) Ę(!) E3, 13) E211-1) A = 13