Chapter 8 - Independence, Basis, and Dimension for Subspaces of (R^n)

Section 8.3 - Basis and Dimension for Subspaces of (R^n)

Example 8.3.1

A={{-1,5,2,9,-3},{4,1,-6,0,7},{3,6,-4,9,4}};

RowReduce[A]//MatrixForm

RowReduce[Transpose[A]]//MatrixForm

Example 8.3.2

(RandMat=RandomReal[{-1,1},{5,9}])//MatrixForm

RowReduce[RandMat]//MatrixForm

RowReduce[Transpose[RandMat]]//MatrixForm

Example 8.3.3

u={-1,5,-2};v={7,-4,3};w={10,6,-9};

A={u,v,w};

RowReduce[A]//MatrixForm

s={8,0,-5};

Join[Transpose[A],Transpose[{s}],2]//MatrixForm

(RowReduce[Join[Transpose[A],Transpose[{s}],2]])//MatrixForm

(ConstVals=Inverse[Transpose[A]].s)//MatrixForm

ConstVals[[1]] u+ConstVals[[2]] v+ConstVals[[3]] w

s.Inverse[A]//MatrixForm