Example 1 (a). Use the back-substitution method to solve the upper-triangular linear system  [Graphics:Images/BackSubstitutionMod_gr_19.gif].  

Solution 1 ( a)

Use the menu "Input" then submenu "Create Table/Matrix/Palette" to enter matrix A and vector B.

[Graphics:../Images/BackSubstitutionMod_gr_21.gif]




[Graphics:../Images/BackSubstitutionMod_gr_22.gif]

[Graphics:../Images/BackSubstitutionMod_gr_23.gif]

Then perform back-substitution.

[Graphics:../Images/BackSubstitutionMod_gr_24.gif]



[Graphics:../Images/BackSubstitutionMod_gr_25.gif]
[Graphics:../Images/BackSubstitutionMod_gr_26.gif]
[Graphics:../Images/BackSubstitutionMod_gr_27.gif]
[Graphics:../Images/BackSubstitutionMod_gr_28.gif]
[Graphics:../Images/BackSubstitutionMod_gr_29.gif]
[Graphics:../Images/BackSubstitutionMod_gr_30.gif]
[Graphics:../Images/BackSubstitutionMod_gr_31.gif]
[Graphics:../Images/BackSubstitutionMod_gr_32.gif]
[Graphics:../Images/BackSubstitutionMod_gr_33.gif]
[Graphics:../Images/BackSubstitutionMod_gr_34.gif]
[Graphics:../Images/BackSubstitutionMod_gr_35.gif]
[Graphics:../Images/BackSubstitutionMod_gr_36.gif]
[Graphics:../Images/BackSubstitutionMod_gr_37.gif]
[Graphics:../Images/BackSubstitutionMod_gr_38.gif]
[Graphics:../Images/BackSubstitutionMod_gr_39.gif]


[Graphics:../Images/BackSubstitutionMod_gr_40.gif]

[Graphics:../Images/BackSubstitutionMod_gr_41.gif]

Verify the solution.

[Graphics:../Images/BackSubstitutionMod_gr_42.gif]



[Graphics:../Images/BackSubstitutionMod_gr_43.gif]

[Graphics:../Images/BackSubstitutionMod_gr_44.gif]

[Graphics:../Images/BackSubstitutionMod_gr_45.gif]

[Graphics:../Images/BackSubstitutionMod_gr_46.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004