Chapter 3 - Gauss-Jordan Elimination and Reduced Row Echelon Form

Section 3.2 - Elementary Matrices

Example 3.2.1

(A={{1,2,3,4},{5,6,7,8},{9,10,11,12}})//MatrixForm

(ET1={{0,0,1},{0,1,0},{1,0,0}})//MatrixForm

ET1.A//MatrixForm

ET1.ET1//MatrixForm

Example 3.2.2

(ET2={{1,0,0},{0,-5,0},{0,0,1}})//MatrixForm

ET2.A//MatrixForm

(FT2={{1,0,0},{0,-1/5,0},{0,0,1}})//MatrixForm

ET2.FT2//MatrixForm

Example 3.2.3

(ET3={{1,0,0},{-3,1,0},{0,0,1}})//MatrixForm

ET3.A//MatrixForm

(FT3={{1,0,0},{3,1,0},{0,0,1}})//MatrixForm

ET3.FT3//MatrixForm

Example 3.2.4

(A={{1,2,-1,6},{2,-1,3,7},{0,4,5,-2}})//MatrixForm

(E1={{1,0,0},{-2,1,0},{0,0,1}})//MatrixForm

E1.A//MatrixForm

(E2={{1,0,0},{0,-1/5,0},{0,0,1}})//MatrixForm

E2.E1.A//MatrixForm

(E3={{1,-2,0},{0,1,0},{0,0,1}})//MatrixForm

E3.E2.E1.A//MatrixForm

(E4={{1,0,0},{0,1,0},{0,-4,1}})//MatrixForm

E4.E3.E2.E1.A//MatrixForm

(E5={{1,0,0},{0,1,0},{0,0,1/9}})//MatrixForm

E5.E4.E3.E2.E1.A//MatrixForm

(E6={{1,0,-1},{0,1,0},{0,0,1}})//MatrixForm

E6.E5.E4.E3.E2.E1.A//MatrixForm

(E7={{1,0,0},{0,1,1},{0,0,1}})//MatrixForm

E7.E6.E5.E4.E3.E2.E1.A//MatrixForm

RowReduce[A]//MatrixForm

(E76={{1,0,-1},{0,1,1},{0,0,1}})//MatrixForm

E76.E5.E4.E3.E2.E1.A//MatrixForm