Example 1 (b). Use the back-substitution method to solve the upper-triangular linear system  , where and .  

Solution 1 ( b)

Observe that only the element different from the matrix in part (a).  We can make an editorial change of the old matrix to form the new matrix.   

Now make the change.   

Check it out to make sure it was changed.  

Remark.  If you like numerical solutions, then make the matrix and vector into decimal form.
If you do not do this you will obtain fractional answers.

Then perform back-substitution.

Verify the solution.

Are you happy with the few digits that are displayed ?
Usually they are enough for educational purposes.  

If you want more, then you will need to learn that computations are done with 16 digit accuracy.  The digits are always there, but just not displayed.

What if you are a "digit" freak and wanted more digits ?

What computer languages have double precision, triple precision, quadruple precision, "infinite" precision in its numerical answers ?

(c) John H. Mathews 2003