Question

b) fina rank A and basis for col A

c) find basis for Nul A

Ti 2017 Let A = 2 3 1 1 3 5 1 2 Find the reduced row echelon form of A.

Answer 1

Let A= 201 2 3 11 be perform row operations on a to make it reduced row echelon form as follows (-2) R, 4R2 R2 3 R1 + R3 R3 2 6 2 EVROTRL TO 0-1 Rqthz -> R3 ! do- O (+2) R2+RIRI o 0 This is reduced row echelon form of the mattina 0 2-1 RREFOF A is 용중해 65 Rank of A=2 because in RREF of a there are two non zero row) and basis for colla) = - {12} reading [The exlumm space of a matrix which contain I in RREF of the matrin À will be the basis for the column space of A. (since in RREF of A, the 14 and 2nd column colein leading 1)] we solve by matria equation as c) 24 60- 10 2 -1 1 $][] → 34+2%3-sey x2-rztky O both side we compairing get 4 + 2Mz-nu=0 = x1=-24z tay 32-33 try=0 Hexe x3 and xey are free variables. let Az = t, ng=s, where tand of are non zero real nomben. x2 = 23-ny

X = -2t+8 22=ts 13=t is x = 31 X2 NB nu Fat+87 t-s t 24us + HI 0 Hence, the basis for Nul(A) =