Question

4 ? 31 NW Let A= 3 7 -8 6 a) Find a spanning set of Nul A. How about Col A? b) is ū in Nul A? Is u in Col A? c) is ù in Nul A? Is ū in Col A? d) Is Col A =İR ?

Answer 1

tit, n=1971) ++ []) ==0) het, a= [2 1-2 L3 4 -5 -2 17 7 3 7 -8 61 ww (a) het, LE Nulla hen 72 - 2 1-2 | 3 4 -5 7 -2 17 7 3 -8 6 274 +4ng - 2013 + hy -274-5m2 +793 +3 +4 = 324 + 7 n. 8x2+604 tie. 274 +42-2nątry = 0 - 0 -284 - 5m2 + 7m2 + 3ny =0 @ 3.04 +792 -87+6ny = 0 - 3 Coefficient matrix of the above system of equation apply [2 4 -2 11 A = -2 -5 1 3 1 and new L3 7 -8 6 . elementary row operahöm on A. A R2 + Rp -2 4 -2 17 0 -1 5 4 R3+ (-2), lo 5 / Rg + R2 T2 4 -2 17 TO -1.54 Lo 00.

Then we have 204 + 42 -213 + My = 0 -M2 +5mg +404 30 17 ny so oor, ny =0 n2 = 503 204 + 4(503) – 202 +020 or, 34 = -90g T nr - 1 MzEIR 5m3 193 = 33 ケンブ ny I So, Nulla = 8 ColA = GIA = Stem { Spom k - 61.J.Lal} 2 Now we consider the mater B = [ 2 -2 31 I Ý - 5 7 1 -2 : 7 -8 and apply elementary row operations on B. Ti 3 67 R₂+(-4) R1 B - 4 - 5 7 * o -17 -14 - 27 -8 Rg+(2) R O 113 14 L2 -2 3] Ry+(-278, Lo -8 -9] Ti 36 l te 13.67 R₂ + Ry 3- O -17-14 lo-19-14 To 5 -5 | LO-8 -9J Lo -8 -9 rio91 R, +(-33R3 ri 0 97 0.01 To 0 -31 → 01-1 R4 +(8) R3 Loo -17]. Ry+(17) RZ Rot (17) R2 To -17 -1 0 0 1 Looo

- 2 stom { [i]. [1, 1:3). [:)] Estama . ). 6]} jing Gold = fto{ [:] [:1, :1) so, Cola = show is TO Lo Now. : 1- 3 12:4 -2 11837 - | 3 7 -8 6 10 0 2 - 5 7 31:1-2 Bu, ū ¢ Nulla ŭ is a vector of IR" and ColA is a subspace of IR? so u & Col A. (c) but I FIR? Nulla is a subspace of 1R" You ūNulla Guido a []** [.). []=[] om ا ا a -3 b . --|| qa-b+c=3 "23,6-1 C 3-99 + b ا = 3-9x(3) - 1 - 25

som g [A] +218) +-289 [:]= [] go, e Cola (d) Gola = stan f [], [:] [:)] Consider the relation, .. 2 = 0 1. Z₂20 97, -22 +23=0 ov, z3 =0 [ms p = 0,72-0) por :) :). [8] are lively independent vectors. so, Cold = ir?