CoCalc -- 2018-10-02-154131.sagews

Writing assignment Multi

Project: Mackenzie Green - Math 231 Fall 2018

Path: 2018-10-02-154131.sagews

Views: ⁶⁷

X=matrix(10, 4, [6.5, 5.1, 4.7, 1, 10.9, 5.8, 8.8, 1, 3.2, 2.1, 15.1, 1, 8.7, 8.4, 12.2, 1, 2.1, 2.9, 10.6, 1, 2.3, 1.2, 3.5, 1, 7.2, 3.7, 9.7, 1, 7.0, 7.6, 5.9, 1, 13.1, 7.7, 20.8, 1, 8.2, 4.5, 7.9, 1])
X

[6.50000000000000 5.10000000000000 4.70000000000000 1.00000000000000]
[10.9000000000000 5.80000000000000 8.80000000000000 1.00000000000000]
[3.20000000000000 2.10000000000000 15.1000000000000 1.00000000000000]
[8.70000000000000 8.40000000000000 12.2000000000000 1.00000000000000]
[2.10000000000000 2.90000000000000 10.6000000000000 1.00000000000000]
[2.30000000000000 1.20000000000000 3.50000000000000 1.00000000000000]
[7.20000000000000 3.70000000000000 9.70000000000000 1.00000000000000]
[7.00000000000000 7.60000000000000 5.90000000000000 1.00000000000000]
[13.1000000000000 7.70000000000000 20.8000000000000 1.00000000000000]
[8.20000000000000 4.50000000000000 7.90000000000000 1.00000000000000]

T=transpose(X)
T

[6.50000000000000 10.9000000000000 3.20000000000000 8.70000000000000 2.10000000000000 2.30000000000000 7.20000000000000 7.00000000000000 13.1000000000000 8.20000000000000]
[5.10000000000000 5.80000000000000 2.10000000000000 8.40000000000000 2.90000000000000 1.20000000000000 3.70000000000000 7.60000000000000 7.70000000000000 4.50000000000000]
[4.70000000000000 8.80000000000000 15.1000000000000 12.2000000000000 10.6000000000000 3.50000000000000 9.70000000000000 5.90000000000000 20.8000000000000 7.90000000000000]
[1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000]

Y = matrix(10, 1, [85.1, 106.3, 50.2, 130.6, 54.8, 30.3, 79.4, 91.0, 135.4, 89.3])
Y

[85.1000000000000]
[106.300000000000]
[50.2000000000000]
[130.600000000000]
[54.8000000000000]
[30.3000000000000]
[79.4000000000000]
[91.0000000000000]
[135.400000000000]
[89.3000000000000]

A=T*X
A

[596.380000000000 402.630000000000 759.640000000000 69.2000000000000]
[402.630000000000 295.460000000000 520.580000000000 49.0000000000000]
[759.640000000000 520.580000000000 1224.94000000000 99.2000000000000]
[69.2000000000000 49.0000000000000 99.2000000000000 10.0000000000000]

B=T*Y
B

[6908.13000000000]
[4878.10000000000]
[9202.55000000000]
[852.400000000000]

M=(A.inverse())*B
M

[ 3.98295856402388]
[ 7.59666694645549]
[0.802072495666959]
[ 12.4976995423068]

F=transpose(M)
F

[ 3.98295856402388  7.59666694645549 0.802072495666959  12.4976995423068]

P=F*T
P

[80.8996723650197 107.030854141478 53.3074622193108 120.746725846678 51.3942151255476 33.5817583101427 77.0627721131336 102.845306007971 139.851900128600 85.6793337421213]

N=matrix(3,4,[9.8,6.2,3.9,1,3.8,6.7,14.5,1,8.1,3.0,10.0,1])
N

[9.80000000000000 6.20000000000000 3.90000000000000 1.00000000000000]
[3.80000000000000 6.70000000000000 14.5000000000000 1.00000000000000]
[8.10000000000000 3.00000000000000 10.0000000000000 1.00000000000000]

N*(transpose(F))

[101.758111270866]
[90.1606618140203]
[75.5703897069363]

X = transpose(matrix(10, 4, [6.5, 5.1, 4.7, 1, 10.9, 5.8, 8.8, 1, 3.2, 2.1, 15.1, 1, 8.7, 8.4, 12.2, 1, 2.1, 2.9, 10.6, 1, 2.3, 1.2, 3.5, 1, 7.2, 3.7, 9.7, 1, 7.0, 7.6, 5.9, 1, 13.1, 7.7, 20.8, 1, 8.2, 4.5, 7.9, 1]))
X

[6.50000000000000 10.9000000000000 3.20000000000000 8.70000000000000 2.10000000000000 2.30000000000000 7.20000000000000 7.00000000000000 13.1000000000000 8.20000000000000]
[5.10000000000000 5.80000000000000 2.10000000000000 8.40000000000000 2.90000000000000 1.20000000000000 3.70000000000000 7.60000000000000 7.70000000000000 4.50000000000000]
[4.70000000000000 8.80000000000000 15.1000000000000 12.2000000000000 10.6000000000000 3.50000000000000 9.70000000000000 5.90000000000000 20.8000000000000 7.90000000000000]
[1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000]

L=X.rows()
L[3:3] = [((x*y) for (x,y,z,w) in X.columns())]
Xnew = matrix(L)
Xnew

[6.50000000000000 10.9000000000000 3.20000000000000 8.70000000000000 2.10000000000000 2.30000000000000 7.20000000000000 7.00000000000000 13.1000000000000 8.20000000000000]
[5.10000000000000 5.80000000000000 2.10000000000000 8.40000000000000 2.90000000000000 1.20000000000000 3.70000000000000 7.60000000000000 7.70000000000000 4.50000000000000]
[4.70000000000000 8.80000000000000 15.1000000000000 12.2000000000000 10.6000000000000 3.50000000000000 9.70000000000000 5.90000000000000 20.8000000000000 7.90000000000000]
[33.1500000000000 63.2200000000000 6.72000000000000 73.0800000000000 6.09000000000000 2.76000000000000 26.6400000000000 53.2000000000000 100.870000000000 36.9000000000000]
[1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000 1.00000000000000]

transpose(Xnew)

[6.50000000000000 5.10000000000000 4.70000000000000 33.1500000000000 1.00000000000000]
[10.9000000000000 5.80000000000000 8.80000000000000 63.2200000000000 1.00000000000000]
[3.20000000000000 2.10000000000000 15.1000000000000 6.72000000000000 1.00000000000000]
[8.70000000000000 8.40000000000000 12.2000000000000 73.0800000000000 1.00000000000000]
[2.10000000000000 2.90000000000000 10.6000000000000 6.09000000000000 1.00000000000000]
[2.30000000000000 1.20000000000000 3.50000000000000 2.76000000000000 1.00000000000000]
[7.20000000000000 3.70000000000000 9.70000000000000 26.6400000000000 1.00000000000000]
[7.00000000000000 7.60000000000000 5.90000000000000 53.2000000000000 1.00000000000000]
[13.1000000000000 7.70000000000000 20.8000000000000 100.870000000000 1.00000000000000]
[8.20000000000000 4.50000000000000 7.90000000000000 36.9000000000000 1.00000000000000]

V=Xnew*(transpose(Xnew))
V

[596.380000000000 402.630000000000 759.640000000000 3769.19500000000 69.2000000000000]
[402.630000000000 295.460000000000 520.580000000000 2630.33500000000 49.0000000000000]
[759.640000000000 520.580000000000 1224.94000000000 4741.29700000000 99.2000000000000]
[3769.19500000000 2630.33500000000 4741.29700000000 25602.5379000000 402.630000000000]
[69.2000000000000 49.0000000000000 99.2000000000000 402.630000000000 10.0000000000000]

V.inverse()

[  0.0988506487892504   0.0750256543960213   0.0101068676527365  -0.0164029183934547   -0.491501620001597]
[  0.0750256543960204    0.188741026657334   0.0206077972602928  -0.0227052977240743   -0.734254505599100]
[  0.0101068676527364   0.0206077972602928  0.00781509021307505 -0.00312231493291073   -0.122729659502290]
[ -0.0164029183934546  -0.0227052977240744 -0.00312231493291074  0.00366126387348386    0.108324050927064]
[  -0.491501620001594   -0.734254505599102   -0.122729659502291    0.108324050927064     3.95506524763297]

U=transpose(Y)*(transpose(Xnew))
U

[6908.13000000000 4878.10000000000 9202.55000000000 43749.6870000000 852.400000000000]

Pnew=U*(V.inverse())
Pnew

[  5.28620555785938   9.40065147489452   1.05014710364325 -0.290895255484557   3.89112171606303]



transpose(Pnew*Xnew)

[81.4872940319212]
[106.885437311445]
[54.4507527466484]
[120.399751852190]
[51.6140498574794]
[30.2028202266270]
[79.1711894889912]
[103.059752149994]
[138.025886215761]
[87.1030661189368]

N=matrix(3,4,[9.8,6.2,3.9,1,3.8,6.7,14.5,1,8.1,3.0,10.0,1])
N

[9.80000000000000 6.20000000000000 3.90000000000000 1.00000000000000]
[3.80000000000000 6.70000000000000 14.5000000000000 1.00000000000000]
[8.10000000000000 3.00000000000000 10.0000000000000 1.00000000000000]

transpose(N)

[9.80000000000000 3.80000000000000 8.10000000000000]
[6.20000000000000 6.70000000000000 3.00000000000000]
[3.90000000000000 14.5000000000000 10.0000000000000]
[1.00000000000000 1.00000000000000 1.00000000000000]

L=transpose(N).rows()
L[3:3] = [((x*y) for (x,y,z,w) in transpose(N).columns())]
Nnew = matrix(L)
Nnew

[9.80000000000000 3.80000000000000 8.10000000000000]
[6.20000000000000 6.70000000000000 3.00000000000000]
[3.90000000000000 14.5000000000000 10.0000000000000]
[60.7600000000000 25.4600000000000 24.3000000000000]
[1.00000000000000 1.00000000000000 1.00000000000000]

Pnew*Nnew

[100.400753308398 94.7840075159123 78.3440574875653]