use(linalg): use(plot): use(matrix): use(RGB) Warning: Identifier 'htranspose' is not exported because it already has a value. Warning: Identifier 'transpose' is not exported because it already has a value. Warning: Identifier 'hilbert' is not exported because it already has a value. [u Warning: Identifier 'Pyramid' is not exported because it seems to be protected. Warning: Identifier 'hull' is not exported because it already has a value. [use] Warning: Identifier 'Integral' is not exported because it seems to be protected. Warning: Identifier 'subs' is not exported because it already has a value. [use] Warning: Identifier 'subsex' is not exported because it already has a value. [us Warning: Identifier 'info' is not exported because it already has a value. [use] Warning: Identifier 'random' is not exported because it already has a value. [us 1) a) Matriu augmentada(M): M:=matrix([[2,6,-2],[2,-4,1],[0,0,1]]) ! $ 2 6 −2 " % #2 − 4 1 & 0 0 1 Amb coordenades homogènies. X:=matrix([x1,x2,1]) ' ( x1 x2 1 eq:=X=matrix([[2,6,-2],[2,-4,1],[0,0,1]])*matrix([x1,x2,1]) ' ( !2 x1 + 6 x2 − 2 $ " % x1 # & x2 = 2 x1 − 4 x2 + 1 1 1 solve(eq,{x1,x2}) )* ,5+ 4+ , x2 = ++ x1 = ++ 17 17 b) T1:= matrix([4,7,1]) . / 4 7 1 M*T1; ' ( 48 − 19 1 M*matrix([48,-19,1]) M*matrix([48,-19,1]) ' ( − 20 173 1 c) A:=matrix([1,5]); B:= matrix([4,7]) 0 1 1 5 0 1 4 7 AB:= B-A; 0 1 3 2 norm(AB,2) 2++ + 13 ABH:=matrix([3,2,0]) ' ( 3 2 0 segm1:=Curve2d([1+3*t,5+2*t], Color= RGB::Pink, t=0..1); plot::Curve2d([3 t + 1, 2 t + 5], t = 0 ..1) vectortrans:= M*ABH ' ( 18 −2 0 MAB:= matrix([18,-2]) . / 18 −2 norm(MAB,2); 2++ + 2 82 Longitud del vector. vector:=Arrow2d([0,0],[3,2]); plot::Arrow2d([0, 0], [3, 2]) vectortrans:=Arrow2d([0,0],[18,-2]) plot::Arrow2d([0, 0], [18, − 2]) plot({vector,Color=Red},{vectortrans,Color=Blue}) plot({vector,Color=Red},{vectortrans,Color=Blue}) y 2 1 0 2 4 6 8 10 12 14 16 18 x -1 -2 reset() use(linalg); Warning: Identifier 'htranspose' is not exported because it already has a value. Warning: Identifier 'transpose' is not exported because it already has a value. Warning: Identifier 'hilbert' is not exported because it already has a value. [u 2 a) eq1:= A*0.025+M*0.025+L*0.025+P*0.025=754; 0.025 A + 0.025 L + 0.025 M + 0.025 P = 754 eq2:= A*0.025+M*0.02+L*0.029+P*0.029=854; 0.025 A + 0.029 L + 0.02 M + 0.029 P = 854 eq3:= A*0.025+M*0.025+L*0.02=546; 0.025 A + 0.02 L + 0.025 M = 546 b) eq4:= total*0.025=754; 0.025 total = 754 solve(eq4) {[total = 30160.0]} c) sol:=solve([eq1,eq2,eq3],[A,M,L,P]); {[A = 7.2 z − 24720.0, M = 13280.0 − 3.2 z , L = 41600.0 − 5.0 z , P = z ]} SCI amb 1 grau de llibertat d) solve(7.2*z-24720=0); {[z = 3433.333333]} solve(-3.2*z+13280=0); {[z = 4150.0]} solve(41600-5*z=0); {[z = 8320]} Per tal que tots els diners siguin positius z ha de ser més gran que 8320. float(solve(41600-5*z=z)) {[z = 6933.333333]} No seria possible, ja que la z resultant és més petita que 8320. No seria possible, ja que la z resultant és més petita que 8320. e) En Pep serà més gran de 8320. use(linalg) Warning: Identifier 'htranspose' is not exported because it already has a value. Warning: Identifier 'transpose' is not exported because it already has a value. Warning: Identifier 'hilbert' is not exported because it already has a value. [u 1) A:=matrix([[0.6,0.3,0.18,0.1],[0.1,0.4,0.1,0.2],[0.1,0.1,0.52,0.2],[0.2,0.2,0.2, ! $ 0.6 0.3 0.18 0.1 "0.1 0.4 0.1 0.2 % # & 0.1 0.1 0.52 0.2 0.2 0.2 0.2 0.5 2) veps:=eigenvectors(A);vaps:=eigenvalues(A); veps:=eigenvectors(A);vaps:=eigenvalues(A); ' ' '! $** ( (' ( ( 0.6059335404 (( ( ( " % + + 0.3602475035 ()1.0, 1, ) # &,,, ( ( (0.42, 1, 0.4347814698 ( ( ( ( 0.5603850055 ) ) '! $** 0.7071067812 (" %++ − 16 − 24 % (" ++ ( " − 6.290905623 10 + 1.464715605 10 i %++ (" %++, (" %++ ( % − 0.7071067812 (" " %+ ++ + )# &,, − 6.77482144 10 − 16 + 7.210907595 10 − 25 i ' ( ( ( (0.3 + 0.000000001114214996 i, 1, ( ( ( ) '! 0.7071067812 $** (" %++ ( " − 0.7071067812 + 0.000000001313114966 i %++ (" %++ (" %++, (" %++ − 17 ( " + 0.000000006565574828 i % ( " 9.405945997 10 %+ ++ + )# &,, − 1.655311036 10 − 16 − 0.000000007878689794 i ' ( ( ( (0.3 − 0.000000001114214996 i, 1, ( ( ( ) '! 0.7071067812 $*** (" %+++ ( " − 0.7071067812 − 0.000000001313114966 i %+++ (" %+++ (" %+++ (" %+++ − 17 ( " 6.931022274 10 +++ − 0.000000006565574828 i % (" %+++ )# &,,, − 2.060907277 10 − 16 + 0.000000007878689794 i {0.42, 1.0, 0.3 − 0.000000001114214996 i, 0.3 + 0.000000001114214996 i} abs(vaps[1]);abs(vaps[2]);abs(vaps[3]);abs(vaps[4]); 0.42 1.0 0.3 0.3 Vap dominant és 1. Vap dominant és 1. 3) L'adenina és 4274. X:=matrix([3313,2800,3500,5000]) ! $ 3313 "2800 % # & 3500 5000 A*A*X ! $ 4274.964 " 2743.95 % # & 3344.706 4249.38 4) Vap dominant=1; solve(14613=alpha1*(veps[1][3][1][1]+ veps[1][3][1][2]+veps[1][3][1][3]+veps[1][ {[alpha1 = 7450.48996]} 7450.48996*veps[1][3][1][1]; // adenina 4514.501759 7450.48996*veps[1][3][1][2] //timina 2684.020408 7450.48996*veps[1][3][1][3] //citosina 3239.334975 7450.48996*veps[1][3][1][4] //guanina 4175.142857