**An Example of a
Numerical-method Solution in**

**The Keys to Linear
Algebra**

As an example of reversing a vector in problem
solving, recall, from Section 1.1.3, the vector **a**
= (25, 32, 20, 22, 28) that represents the ages of five patients.
Suppose you have a method for sorting the components of a vector
in increasing order, but that you now want to sort the components
in decreasing order. Rather than writing a new sorting procedure,
you can can use the existing one by performing the following
steps:

**Step 1**. Reverse
the vector **a** to obtain -**a** =
(-25, -32, -20, -22, -28).

**Step 2**. Sort the vector -**a
**in increasing order: (-32, -28, -25, -22, -20).

**Step 3**. Reverse the vector in
Step 2 to obtain (32, 28, 25, 22, 20),

which is the original vector sorted in decreasing order.

The three steps just described for sorting the
components of a vector in decreasing order are an example of a **numerical-method
solution**, which is a solution obtained from the problem
data by performing a sequence of computations.