NotebookDirectory[]

mX=Transpose[{{1,1,1,1},{2,3,5,6}}]

vy={3,2,1,0}

Transpose[mX].mX

Det[{{4,16},{16,74}}]

Transpose[mX].vy

Inverse[Transpose[mX].mX]

Inverse[Transpose[mX].mX].(Transpose[mX].vy)

{(43/10),-(7/10)}.{1,x}

Transpose[{Transpose[mX][[2]],vy}]

Point[#]&/@Transpose[{Transpose[mX][[2]],vy}]

Plot[{{(43/10),-(7/10)}.{1,x},{4,-(2/3)}.{1,x},{(13/3),-(2/3)}.{1,x},{(12.5/3),-(2/3)}.{1,x}},{x,0,7},PlotStyle->{Blue,Green,Gray,Red},Epilog->{{RGBColor[0,0.5,0],PointSize[0.015],Point[#]&/@Transpose[{Transpose[mX][[2]],vy}]}}]

Transpose[mX][[2]]

({(43/10),-(7/10)}.{1,x})/.{{x-> 2},{x-> 3},{x-> 5},{x-> 6}}

vy

(({(43/10),-(7/10)}.{1,x})/.{{x-> 2},{x-> 3},{x-> 5},{x-> 6}})-vy

{-(1/10),(1/5),-(1/5),(1/10)}

(Sqrt[{-(1/10),(1/5),-(1/5),(1/10)}.{-(1/10),(1/5),-(1/5),(1/10)}])

(({((12+(1/2))/3),-(2/3)}.{1,x})/.{{x-> 2},{x-> 3},{x-> 5},{x-> 6}})

(({((12+(1/2))/3),-(2/3)}.{1,x})/.{{x-> 2},{x-> 3},{x-> 5},{x-> 6}})-vy

(Sqrt[{-(1/6),(1/6),-(1/6),(1/6)}.{-(1/6),(1/6),-(1/6),(1/6)}])

PrimeQ[20190731]

C6S6Problem4=Plot[{{(43/10),-(7/10)}.{1,x},{4,-(2/3)}.{1,x},{(13/3),-(2/3)}.{1,x},{(12.5/3),-(2/3)}.{1,x}},{x,0,7},PlotStyle->{Blue,RGBColor[0,0.75,0],Gray,Red},Epilog->{{RGBColor[0,0.5,0],PointSize[0.01],Point[#]&/@Transpose[{Transpose[mX][[2]],vy}]}},
Prolog->{{Thickness[0.001],GrayLevel[0.5],Dashing[{0.005,0.005}],Line[{{-2,1.5},{12,1.5}}],Line[{{4,-3},{4,15}}]}},

PlotRange->{{-0.3,7.1},{-0.3,4.5}},Frame->False,AspectRatio->Automatic,ImageSize->600]

SetDirectory["C:\\Dropbox\\Work\\myweb\\Courses\\Math_pages\\Math_304\\Pictures"]

Export["C6S6Problem4.png",C6S6Problem4,"PNG",ImageResolution-> 1200,ImageSize->600,"CompressionLevel"->0]