Example 2. Use the forward-substitution method to solve the lower-triangular linear system  [Graphics:Images/BackSubstitutionMod_gr_103.gif].  

Solution 2.

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

[Graphics:../Images/BackSubstitutionMod_gr_104.gif]




[Graphics:../Images/BackSubstitutionMod_gr_105.gif]

[Graphics:../Images/BackSubstitutionMod_gr_106.gif]

Then perform forward-substitution.

[Graphics:../Images/BackSubstitutionMod_gr_107.gif]



[Graphics:../Images/BackSubstitutionMod_gr_108.gif]

Verify the solution.

[Graphics:../Images/BackSubstitutionMod_gr_109.gif]



[Graphics:../Images/BackSubstitutionMod_gr_110.gif]

[Graphics:../Images/BackSubstitutionMod_gr_111.gif]

[Graphics:../Images/BackSubstitutionMod_gr_112.gif]

[Graphics:../Images/BackSubstitutionMod_gr_113.gif]

To do it in decimals, you can enter decimal values in the matrix and vector.

[Graphics:../Images/BackSubstitutionMod_gr_114.gif]

[Graphics:../Images/BackSubstitutionMod_gr_115.gif]
[Graphics:../Images/BackSubstitutionMod_gr_116.gif]

But why require yourself to type all those decimal points ?
The same thing could be accomplished by using the convert to numerical function, that's the reserved word  [Graphics:../Images/BackSubstitutionMod_gr_117.gif].

[Graphics:../Images/BackSubstitutionMod_gr_118.gif]

[Graphics:../Images/BackSubstitutionMod_gr_119.gif]
[Graphics:../Images/BackSubstitutionMod_gr_120.gif]

[Graphics:../Images/BackSubstitutionMod_gr_121.gif]

[Graphics:../Images/BackSubstitutionMod_gr_122.gif]
[Graphics:../Images/BackSubstitutionMod_gr_123.gif]



[Graphics:../Images/BackSubstitutionMod_gr_124.gif]


[Graphics:../Images/BackSubstitutionMod_gr_125.gif]

Verify the solution.

[Graphics:../Images/BackSubstitutionMod_gr_126.gif]



[Graphics:../Images/BackSubstitutionMod_gr_127.gif]

[Graphics:../Images/BackSubstitutionMod_gr_128.gif]

[Graphics:../Images/BackSubstitutionMod_gr_129.gif]

[Graphics:../Images/BackSubstitutionMod_gr_130.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004