Fenômenos Químicos e Físicos

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<p>1 a) = T(v) +T(u) ii) = T(0+0) = + = K. 0 + b) Se items i) ii) 2 T.L.? a) u= T Y2 = = = ] i) = = T [ = = : = T.L. R ) = (Y1+Y2)] (Y1+Y2) ] = = i) = = = = = KT(v) ET.L</p><p>c) h: M2 R T d b ] = det = (ad - 1) T(u+v) = T(u) + T + C2 d2 = T ) = (d2+d2) - (CL+C2) = + a2d2)+ - = [ + - = T(u) + T(v). ii) T(KN) = T b2 d2 1) = T Ka2 Kb2 1) = - = I K - ] = K = K.T(v) ET.L</p><p>= bx2+ex) + = + = = T(KV) = = = + = + = = T.L = 0-1 = + = T = ( 2 now da para the</p><p>N: IR IR 1x2+x2 T(u) = 1x1 + T (v) T(u) ou / saw r logo e T.L. 11)</p><p>3 a) T(1,0,0)= (20) = (1,1) T(0,0,1) = (0,-1) + = # Y-Z) # 4 b) = # = T(0,1) = T(0,-2) c) b=x-y 3a=x a=x 2a+b=y = + + = + = # = = = # (3,2,1) + = (3,2,1) = (3a, = d=0</p><p>T: IR 3 d) T R R 3 IR& = = 0 - = (a,a-2b) x A. 01 . = a=x 2x2 2 2 a-2b=y + (0,-2) (x,x) + -x+y) = x-x+y) = = (1,1) = = (3,1) = (a,a-2b) Sa=1 1-2b=1. b=0 =</p><p>T:U V co(v) # Im(T) {T(us) = T + + cuk) = au, bu2= = = # 10 T= ? [R] = = = 211 = 404 02 415 0-11 3x3 = 3x3 404 = 3x3 3x1 T(v) = (0,1,0) + = # = = = 1 2 -5/2</p><p>11 HR a) 10 A.[v]= a 2 2 2 = (a,-a+2b) = X Sa=x 3x+Y b=y+x 2 2 X+Y 2 x(1,0,-1)+ = 2 2 IR2 IR (-2,2,1) = (-2,2,1) = b+2c=2 101-2 101-2 0122 of -a+2b=1 0122 021-1 (4,-2,0) = 1014 d=4 012-2 =D 012-2 1200 0214 00-30 in -11 12 =</p><p>c) 10 01 10 2 3x2 + (0,1,0) + = a=1 = + T(0,2) = (0,0,1) GEO D (0,1,0), (0,0,1) } C2=1 # 12 = R : IR 2 IR2 212 2x3 R.S = = (5x+2y+z) (1,0) + = #</p><p>13 R: IR 2 = = 3x2 2x3 = = a=2, b=1; # b) = S(0,1,0)=(1,0) 3x2 [SOR] = # 14 T = (a+d,b+c) B= / a) T =</p><p>IR2 V 2 = ) A.v = 2 1 (2x+y) (x-y) 4x2 -1 1 -x Y (2x+y) = = 00 + (x-y) 00 10 + Y + + + 2x+y Y = = 2a+b a-b -a b 2a+b -a a-b b = 1 a-b = (F) a=o b=1 SI b=1 ha i possivel (ab) uma igualdade logo</p><p>15 T: 122 [T] = a) u (x,y) 0 -2 + { = x 2y Logo u= (x,y)= (x,-x) # b) v=? - = y) { a x Logo NEO # 16 a) E KEIR i) T(u) + T(v) = T(u+v) EW ii) KT(u) = EW > hogo Im(+) e S.V de W. b) Sexam u, v E K = ii) = T(uk)=0 ker(T) de V.</p><p>17 W S: V S(v) = T: V W = (v) = a) i) = + = + + + T(V2) = + + = ii) = = = Logo S+T i T.L # b) v) = T(u) = + = a + a = = a N = K = hogs. # e) X= {T IT:V Syam T(v), T(u) EIR i) + T(u) = E ii) K. = E x 8 prop de EV.</p><p>d) 2 W dim W=3 = = 6 18 : = = O T(v) = 2 = 2 2 =0 2 x+2x in Im(T) = / > dimIm(T) = 2 S(v) = => x (0,1,1) + Y (2,-1,0) = dim = 2 + Im($) = dim + 2 = 2 + Im(T) = + 2 =</p><p>19 a) Ker(T) : = = (z,x-y, -z) = x(3,1,0) = base de # b) dimIm(T) = ? 010 10-1 10-1 0-10 010 Im(T) LD 010 1.0-1 000 = (0,1,0) + + Z (1,0,-1) (0,1,0)} é base de Im(T) = dimIm(T) = 2 # 1 + = 3 = e) Im(T) = CD (T) dim Im(T) = 2 # Logo now e d) )</p><p>21 T: P3 P3 D at bx + T(v) = a2 + + a) + = + x + base de P3 b) = b2 + 2C2X + i) = ] = + + = + x2 = + + + = ii) = KT(u) = + [ K + = i T.L. # 2 = EP3 Ker(T)= = K {L} base dim 1 ast + (1,0,0) + Co, 2, + a4 (0,0,3) (T) = 3 {s, base de Im(+) #</p><p>22 D: P3 P3 i v= D(v) = > D = 11 + = + = D(u) + D = D(p(x)) = = T.L. T(v) = =0 (2c)+ + 3dx2 { C=O 2C + 6 dx 6d=0 DE P3 D = 0,0) = K1 + K2 (0,1,0,0) base de</p><p>23 = 40 20 B= 0-4 3x2 40 2y+ 2a-b=y 3x2 -0-4 4y+2x = 4 2 2 = 8y+4x 2y+x 4 = 2y+x -2x 2 2 4 4 5(x,y) = 2 = + = = -2y-3x) 2 = #</p><p>24 tem bases, B : {(1,0,0), Para A : Para = Y 3x3 3x1 3x2 3x1 A(v)= = 2y (0,1,0) + = = Ker TA = 0=0 ImTAi {(1,2,13} = LD -x) = = = 100 de 01 = Im = 06 by (0,6y, 0-1 -Y de {(s,0)} de</p>