Question

please can you give the solutions not just anwsers. Thank you.

1 LetE CR E : x + x2 - X3 = 1, be an affine subspace. Select one or more: 1. The affine subspace ECR is passing through the point (0,3,2) il E = aff((1,0,0), (2,0,1),(1, 1, 1)) l. The affine subspace H CR' perpendicular to E and passing through the point (1,2,3) is given by H -(1,2,3) + lin((3,3, -3)) W. The Image of the affine orthogonal projection of the point p = (2,0, -1) onto the affine subspace Els equal to (1.2.1) 20 Leto: R2 R? be a linear transformation given by the formula p((x1, x2)) = (x1 + x2, x1 + 2x2). Let A = ((0,1),(1,1)), B = ((1,0).(1.-1)) are (ordered) bases of R? Select one or more: Mga)! = 1 1 If coordinates of vector v € R2 relative to basis A are equal to 0,1, then coordinate of vector (1) relative to basis Bare equal to 0,0 H. ((XI.2) = (2x1 + 3x2, 3x2 + 5x2) M«•): - (23)

Answer 1

1:42 AM Wed Jun 10 62% < Notes ne C ch aj 0+3.2=1; (0,3,2) EE '(correet!) (ii) E= aff( (1,0,0), (2,0,1), (1,1,1) } (2., 42, 43) E E = (^,,^2, 1₂) TS (d, I s しい 22,3)= x,(1,0, o) ta(2,0, 1) for some de faz(','') such that Exiz =(2, +2&_thy 23, 23, 2q + 2) 2 (lg-k) - L3 = 12;&z=23-12; X=0,- "1-2013 taz 22,+&gt az = a, tlz-xz = EC aff' {(1,0,0), (2,0,1), (1,133 & since (1,0,0),cha1),(1,1) GE=) aff{} CE so option co linear space dz - a 1 is correelr (all c correct & -C (ii) H=(1,2,3)+V; va (0,0) + lin $6,0,1), 8,.,,)} - CW :HI E =) (ah, CGV = (aubec) Iw at C=0 btc=0 b= c-c-c, cl=c(-lilil) =) H=(1,2,3)+lin (3,3,3 (2,0,-1)-(1,0,0) o.p. on W ( let it be =) = {(1, 0,-1),(1,0,1% (1,0,12 + < (1,0,1),(0,', el -c =d(3,3,-3) c ) a= c (a,b,c) ixs Incorre Et el (0,1,1) Tv

cij Il so option co E:*, +%23=1 If E passes through (0,3,2) then 0+3~2 al which is true. is correct (11) E= aff( (1,0,0), (2,0,1), (1,1,1) } (^.,^2,"3) E (1,0,0) ) dal (di (TS しこ」 ^3) = di ta212,0, 1) for some de faz(!,!,!) = (^,,"2,1₂) such that {xi =(2, + 2 kthy, 23, 2q + 2) e) &z= 12; d2=*,-l2 ; &,= *,-2 (Mg-") taz 22 itaqt az = aitla-x, =) EC off {(1,0,0), (2,0,1), (1,1,113 & since so option ( - d2 evin -213 a 1 (1,0,0) (201) 111,11 EE=) aff{ ? CE ) is correels (ii) H= (1,2,3)+r; va linear space 0,0,0) + lin M1,0,!), 0,1423-6 HI E =) (ah,cer (aube C) Iw (alle C correet & El -) o C— О btc=0 a=-c b=-( =c-c-c, c2= c(-1;l,1)=(3,3,-3) =) H=(1,2,3)+lin (3,3,3 (a,b,c) DoTestian (20)