Question

b b2 0 N Exercises 9–12 display a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces.

Answer 1

for, R₂-2R, 12-5 2 s -84 3 -3-9 R3+3Ri 3 10 -7 11 7 'RG-3R, der at Ano novih 0903 we 42-5o 0 1 2 3 S 0-3-6-7-5 4 8 11 0 R, -2R2 8 Į R3. 2 4 5 Tio 20-8-ch 24 5 o 2 2/ R3+3 R2 yulih o 5 o R4-4R2 O 05-10 0 O -9 R4-R3 2 4 R,+8R3 S ooo O 0 ( 2 R2-4R3 o 10 O o O doo 57 1-3 2 ER آن را بداند - 0 o 22 - Erzestra sts - J Now 0 2 0 -3 6 2 0 0 o The egn's are 4-9u3t 5x5=0 x2 + 2x3-3x5=0 xy+205=0

from is and sa /18 (2 + 4c, nered wor let x=0, AWW x2 =C2 C-9Xzt sag=0 C2 + 243-3x520 1) netzugao 15 %%+27 23 = -36, -15/estions =tser - 1703 E-36,.5e 3 ct 562 or *17 stPapa from il 2% 10 el 349 =0 17 176276G HOLZ or 305 17 HE 127 C2 +6C, ods = 51 962 +26, L 17 onet-new eis and ussidy I EX 2 ** 2 est er .62 + 3 21 U ☺ st ho sing) y == ci WCA) is the ti - ( 8 (י+ רכי - ( ung getre, 12 N(A) = Lşe, ce} = 284, 22}

{x, x2} is a basis of Nula .. 22 to EXO dim Nuld =2 - we have At. 2 s DEEL ) Orust R2-2RI R3+SRI 3 3 -g 10 9-7 -7 11 -2 7 -I 8 4 RS TRI DE -1 3 3-s -3 4 O o 2 -3 3 -3 4 2 -6 8 4 -7 5 -5 10 R, -282 R3-2 R2 0 o -5 R4-4R2 0 0 I 10 0 -10 Rs-SR2 & Rau 0-27 3 -3 4 0 1 R-3R To Rs 6 0 0 - R2+3Rq Rs-Rq o 0 a o o o R (say) R is a rou echeon matrix The non-zero vectors of R are (1,0,0,-2), (0,1,0,1), form a basis of of at ie, of the column space . (0,oo 1,-1). These the rowe space of A and consequently din of cola 3.