2016.01.20 Linear Algebra Class

Quiz #3 Stuff

A = {{-1},{1},{1}};
B = {{1,-1,2},{2,4,0}};
CC = {{2,-3}};

A//MatrixForm

B//MatrixForm

(R = {{1,2,-3},{1,1,0},{2,0,3}})//MatrixForm

A.B

B.A

B.A//MatrixForm

C.B//MatrixForm

CC.CC

A.CC

A.CC//MatrixForm

Plotting Planes and Lines

plane1 = 5x-2y+7z==15;

PlanePlot1 = ContourPlot3D[Evaluate[plane1],{x,-5,5},{y,-5,5},{z,-5,5}]

LinePlot1 = ParametricPlot3D[{3z+4,5z+2,z},{z,-10,10}]

Show[PlanePlot1,LinePlot1]

We want to construct a line in the given plane, so let’s arbitrarily set x = 5z, y = 1+(Sqrt[3]) z.

(5x-2y+7z==15)/.{x-> 5z, y-> Sqrt[3]*z + 1}

Solve[%,z]

Setting x and y to linear functions of z was overkill, we just get a single point back on the plane.

(5x-2y+7z==15)/.{x-> 5z}

Solve[%,y]

LinePlot2 = ParametricPlot3D[{5z,(1/2) (-15+32 z),z},{z,-10,10}, PlotStyle->{{Black, Thickness[0.01]}}]

Show[PlanePlot1,LinePlot1, LinePlot2]

LinePlot3 = ParametricPlot3D[{5z,(1/2) (-15+32 z),z+1},{z,-10,10}, PlotStyle->{{Orange, Thickness[0.01]}}]

Show[PlanePlot1,LinePlot1, LinePlot2, LinePlot3]

LinePlot4 = ParametricPlot3D[{5z+1,(1/2) (-15+32 z),z},{z,-10,10}, PlotStyle->{{Green, Thickness[0.01]}}]

Show[PlanePlot1,LinePlot1, LinePlot2, LinePlot3, LinePlot4]

(I3 = IdentityMatrix[3])//MatrixForm

B.I3//MatrixForm

B//MatrixForm

IdentityMatrix[2]//MatrixForm