Review For Test #1

Items to remember:
(1) You can have ALL the Mathematica notebooks from Chapters 1 though 5.
(2) You can also have any of the Mathematica notebooks from the website from in-lab classes.
(3) No BOOK.  No INTERNET.  No HELP.
(4) It is up to you to have the notebooks ready before the exam begins.
(5)  Time-limit is the usual 50 minutes.

add words to describe what you are doing in mathematica

A = {{3,2,1,0},{-2,3,-4,5},{3,2,-2,7}}

N[RowReduce[A]]//MatrixForm

f = 3x+2y+z ==0;
g = -2x+3y-4z==5;
h = 3x+2y-2z==7;

1.2-2

planeplot = ContourPlot3D[Evaluate[{f,g,h}],{x,-0.8,3.2},{y,-0.64-2,-0.64+2},{z,-4.3,0.3}, MeshStyle->None, ContourStyle->{Red, Gray,Purple}]

sphereplot = Graphics3D[Sphere[{1.2, -0.64,-2.3},0.2]]

Show[{planeplot,sphereplot}, AspectRatio->1]

Anew = {{3,2,1},{-2,3,-4},{3,2,-2}}

B= {{0},{5},{7}}

Join[Anew, B,2]//MatrixForm

Inverse[Anew].B//MatrixForm

RowReduce[A]//MatrixForm

Det[Anew]

Anew//MatrixForm

Anew3 = {{3,2,0},{-2,3,5},{3,2,7}}

Det[Anew3]/Det[Anew]

Anew//MatrixForm

E1 = {{1,0,0},{2/3,1,0},{0,0,1}};

E1.Anew//MatrixForm

E2 = {{1,0,0},{0,1,0},{-1,0,1}};

E2.E1.Anew//MatrixForm

Um = E2.E1.Anew

Lm = {{1,0,0},{-2/3,1,0},{1,0,1}};

Lm.Um//MatrixForm

Anew//MatrixForm

AX = B
(LU)X = B
L(UX) = B
So let Y = UX
So we solve 
(1)  LY = B   (for Y)
then 
(2) UX = Y   (for X)

Y = {{y1},{y2},{y3}};

Lm.Y//MatrixForm

B//MatrixForm

Solve[-((2 y1)/3)+y2 == 5,y2]/.{y1->0}

Solve[y1+y3  == 7,y3]/.{y1->0 ,y2->5}

Ym = {{0},{5},{7}};

X = {{x1},{x2},{x3}};

Um.X//MatrixForm

Solve[-3 x3 == 7,x3]

Solve[(((13 x2)/3)-((10 x3)/3) == 5)/.{x3-> -7/3},x2]

Solve[(3 x1+2 x2+x3==0)/.{x3-> -7/3, x2-> -25/39},x1]