Question

1.2.12. Show that the three types of elementary row operations discussed on p. 8 are not independent by showing that the interchange operation (1.2.7) can be accomplished by a sequence of the other two types of row operations given in (1.2.8) and (1.2.9).

Answer 1

1.28 write Ax-B 3 - J a -3 22 -4 3 write augumented manix and echelon forn. convert into now 3 -2 -3 2 aft, 2 -3 4-3 5 -4 5 -2 - 21-1 Raz-222 ( -1 R Rly -3 -3 Roth -1 sinee rank A=223= rank of Augumented matrix. since runk A & sane Augumented mamix I system has no solufing 1.2g - 3 -2. & -3 a 5 5 w 5 -3 -4 -4 - 5 2 lez-var + - 2 o RER 3 -4 26 -1 +R 2 rank A=2 -rank of Augal mented matrix i solution exist but sank = 2 2 nous ramiabi infinite solution Voist 3-2-1 vanoble free say at and

- ли - (+ 1 - 3-+ҡ3 - 4 X, — «7 from 22 1+x3 promo 24 - 2+2 -2 23 - , +7 (2) - (t) 44 3 + 2ъt-at . 1 +t . (4 ад 23) (att itt, t) ita con tant of t we get solution Дета од ло