{"text_format":"3","workbook":"xlsx","n_sheets":2,"sheets":["Mit_Excel","Mit_R"],"read":"whole","date_system":"1900"}

{"sheet":"Mit_Excel","index":0,"n_rows":57,"n_cols":8,"rows_kept":57}
["Aufgabe a)",null,"X",null,"y","x"]
[null,500,200,0,500,{"$f":"SUM(B2:E2)","v":1200}]
[null,1000,7000,15000,2000,{"$f":"SUM(B3:E3)","v":25000}]
[null,600,700,5000,3000,9300]
[{"$nulls":4},"=MMULT(B7:D9;F2:F4)"]
["Aufgabe b)",null,"R",null,"r"]
[null,3,1,0,{"$f":"MMULT(B7:D9,F2:F4)","v":28600}]
[null,5,0.3,5,60000]
[null,4,2,3,82700]
[{"$nulls":5},"=MMULT(C12:E14;B12:B14)"]
["Aufgabe c)","r1","R^-1","=MINV(B7:D9)",null,"x1"]
[null,500,{"$f":"MINVERSE(B7:D9)","v":0.4080717488789237},0.13452914798206284,-0.22421524663677128,{"$f":"MMULT(C12:E14,B12:B14)","v":15.695067264573993}]
[null,600,-0.22421524663677128,-0.4035874439461884,0.672645739910314,452.9147982062781]
[null,1200,-0.39461883408071746,0.08968609865470849,0.18385650224215247,77.13004484304932]
[null,"Berechnung Technologiematrix A:"]
[{"$nulls":4},"=1/1200","=1/25000","=1/9300"]
[null,null,"X",null,"(diag(x))^-1"]
[null,500,200,0,{"$f":"1/1200","v":8.3333333333333339E-4},0,0]
[null,1000,7000,15000,0,{"$f":"1/25000","v":4e-05},0]
[null,600,700,5000,0,0,{"$f":"1/9300","v":1.0752688172043011E-4}]
[]
[null,"A","Technologiematrix"]
[null,{"$f":"MMULT(B18:D20,E18:G20)","v":0.4166666666666667},0.008,0,"=MMULT(B22:D24;E22:G24)"]
[null,0.8333333333333334,0.28,1.6129032258064515]
[null,0.5,0.028,0.5376344086021505]
[]
[null,"E",null,null,"E-A",null,null,"y1= (E-A)x1"]
[null,1,0,0,{"$f":"B28-B23","v":0.5833333333333333},{"$f":"C28-C23","v":-0.008},0,{"$f":"MMULT(E28:G30,F12:F14)","v":5.5321375186846025}]
[null,0,1,0,{"$f":"B29-B24","v":-0.8333333333333334},{"$f":"C29-C24","v":0.72},{"$f":"D29-D24","v":-1.6129032258064515},188.6161338540914]
[null,0,0,1,-0.5,-0.028,0.4623655913978495,15.133130816336369]
[]
["Aufgabe d)","y2=(E-A)*x2"]
[null,"x2","y2"]
[null,700,{"$f":"MMULT(E28:G30,B34:B36)","v":384.33333333333326}]
[null,3000,-5068.4946236559135]
[null,4120,1470.9462365591398]
[]
[]
["Aufgabe e)"]
[null,"x3=(E-A)^-1*y3"]
[null,"y3","(E-A)^-1",null,null,"x3"]
[null,2650,{"$f":"MINVERSE(E28:G30)","v":1.8175232057957889},0.023364274394385296,0.08150328277111142,{"$f":"MMULT(C42:E44,B42:B44)","v":6359.999999999995}]
[null,10600,7.52773375594295,1.703645007923931,5.942947702060223,132500.00000000003]
[null,15900,2.4213266923251084,0.12843558976681035,2.6108218247679424,49290.000000000015]
[]
[]
["Aufgabe f"]
["X1"]
["diag(x3)"]
[6360,0,0]
[0,132500,0]
[0,0,49290]
[]
["A*Diag(x)=","X1"]
[{"$f":"MMULT(B23:D25,A50:C52)","v":2650},1060,0]
[5300,37100,79500]
[3180,3710,26500]

{"sheet":"Mit_R","index":1,"n_rows":25,"n_cols":1,"rows_kept":25}
["Mit R:"]
["X=matrix(c(500,200,0,1000,7000,"]
["15000,600,700,5000),byrow=T,ncol=3)"]
["y=c(500,2000,3000)"]
["#a)"]
["x=X%*%rep(1,3)+y"]
["#b) "]
["R=matrix(c(3,5,4,1,0.3,2,0,5,3),ncol=3)"]
["r=R%*%x"]
["#c) "]
["r1=c(500,600,1200)"]
["x1=solve(R)%*%r1"]
["A=X%*%solve(diag(as.vector(x)))"]
["(diag(3)-A)%*%x1  #=y1"]
[]
["#d) "]
["x2=c(700,3000,4120)"]
["(diag(3)-A)%*%x2 #=y2"]
[]
["#e) "]
["y3=c(2650,10600,15900)"]
["x3=solve((diag(3)-A))%*%y3"]
[]
["#f) "]
["A%*%diag(as.vector(x3))  #=X1"]