Problem 6 on page 172 (section 5.2)

{-2x+(-4-λ) y ==0,(2-λ) x + 4 y ==0};

{-2x+(-4-λ) y ==0,(2-λ) x + 4 y ==0}/.λ->π/2

Solve[%,{x,y}]

{-2x+(-4-λ) y ==0,(2-λ) x + 4 y ==0}/.λ->22

Solve[%,{x,y}]

A = {{-2,-4-λ},{2-λ,4}};

X = {{x},{y}};

A.X//MatrixForm

Det[A]

Solve[Det[A]==0,λ]

Solve[(A/.{λ->-2}).X==0,{x,y}]

Solve[(A/.{λ->0}).X==0,{x,y}]

A= {{2,3,4},{5,-1,8},{-2,3,6}};

Det[A]

X = {{x},{y},{z}};

B = {{15},{-10},{11}};

Inverse[A].B//MatrixForm

A//MatrixForm

E1 = {{1,0,0},{-5/2,1,0},{0,0,1}};

E1.A//MatrixForm

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

E2.E1.A//MatrixForm

E3= {{1,0,0},{0,1,0},{0,12/17,1}};

(Upps = E3.E2.E1.A)//MatrixForm

(Lows = Inverse[E3.E2.E1])//MatrixForm

Inverse[E1].Inverse[E2].Inverse[E3]//MatrixForm

Lows.Upps//MatrixForm

A==Lows.Upps

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

(Lows.Y==B)

(Lows.Y)[[1,1]]==B[[1,1]]

Solve[((Lows.Y)[[2,1]]==B[[2,1]])/.{y1->15},y2]

(Lows.Y)[[3,1]]==B[[3,1]]

Solve[((Lows.Y)[[3,1]]==B[[3,1]])/.{y1->15,y2->-(95/2)},y3]

YSoln={{15},{-95/2},{-128/17}};

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

Upps.X//MatrixForm

Solve[(Upps.X)[[3,1]]==YSoln[[3,1]],x3]

Solve[((Upps.X)[[2,1]]==YSoln[[2,1]])/.{x3->-(64/73)},x2]

Solve[((Upps.X)[[1,1]]==YSoln[[1,1]])/.{x2->(423/73),x3->-(64/73)},x1]

Inverse[A].B//MatrixForm

This is new stuff on section 5.5

NewA = {{1,6,3,-2},{Sqrt[2],4,3,Sqrt[6]},{7,-3,11,2},{1,2,3,4}};

Det[NewA]

N[%]

Simplify[Inverse[NewA]]//MatrixForm

(NewAAugmentI4 = Join[NewA,IdentityMatrix[4],2])//MatrixForm

Simplify[RowReduce[NewAAugmentI4]]//MatrixForm