Page 33 - A Course in Linear Algebra with Applications

1.2: Operations with Matrices 17

.861 .834 \
.139 .166y

Hence
*-**,-(•£)

so that 8529 of the 10,000 will be in work after three years.
At this point an interesting question arises: what will
the numbers of employed and unemployed be in the long run?
This problem is an example of a Markov process; these pro-
cesses will be studied in Chapter Eight as an application of
the theory of eigenvalues.

The inverse of a square matrix

An n x n matrix A is said to be invertible if there is an
n x n matrix B such that

AB = I n = BA.

Then B is called an inverse of A. A matrix which is not invert-
ible is sometimes called singular, while an invertible matrix is
said to be non-singular.

Example 1.2.9
Show that the matrix

1 3
3 9

is not invertible.

If f , ) were an inverse of the matrix, then we should
have