Chapter Ten — Applications of Matrix Algebra
The Humongous Book of Algebra Problems
226
Note that a
31
already equals 0, but a
32
must equal 0 as well, so apply the row
operation .
To complete row echelon form, use the row operation to make
a
33
= 1.
This is getting
messy. To add 8 in
a
33
and to add 5 in
b
31
, you need to use
common denominators,
so multiply the top
and bottom of these
fractions by 13.
Chapter Ten — Applications of Matrix Algebra
The Humongous Book of Algebra Problems
227
Note: Problems 10.32–10.33 refer to the system of equations defined in Problem 10.32.
10.33 Express the matrix generated by Problem 10.32 in reduced-row echelon form
and identify the solution to the system of equations.
Apply the row operation to make a
23
= 0.
Apply the row operation to make a
13
= 0.
Apply the row operation to make a
12
= 0 and, therefore,
express the matrix in reduced-row echelon form.
The solution to the system is (x,y,z) = (–1,7,–2).
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