Question

Find bases for the four fundamental subspaces of the matrix A. 1 38 A 090 II N(A)-basis III N(AT) = R(A)-basis R(AT)-basis
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Answer 1

Date i 3 8 o fot g for NCA) -Basis solve system 0 where (a,bic) augumented mamx 3 S 3 Calo 5 L 0 g o rank 3-2 <3 = no. of variable variable free say Cat a + 3b toc 라 a =-3b-8cast bo Caibic) = C-stolt ) (-8,0,1) tit=constant A Basis of MCA ) = {(-8, 0112 } AT 1 - اليمن 9 solwe A noi a laib) matrix is augumented 0 Rq3R1 Rz8 g 3 g olo 8 c. C o IL ålz bao CIG S can b) = Cool Basis (AI) -{(0,0)}

for RCAL. ech eron matrix A in to convert form rad echelon forms of a f & o one. column of since first and second column contain leading fix and second original Aromama for ins Basis of LIAN ... Basis RIA laite stul Elodt 3 g. similler RCATO Row echeton form of AT [... both o column contach reading one - RCAT) Basis 9 <<