Page 71 - Statistics and Data Analysis in Geology

Matrix Algebra

If this seems unfamiliar, review the sections in an elementary algebra book that
deal with factoring and quadratic equations. Now, we can try the procedures just
outlined to find the eigenvalues of the 2 x 2 matrix:
A= [17 -16 -"]

45

First, we must set the matrix in the form

Equating the determinant to zero,

-6 l=o
1174 -16-h
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we can expand the determinant

Multiplying out gives

-272 - 17h + 16h + h2 + 270 = 0

which can be collected to give
A2 - h - 2 = 0
This can be factored into
(A - 2) (A + 1) = 0

So, the two eigenvalues associated with the matrix A are

This example was deliberately chosen for ease in factoring. We can try a some-
what more difficult example by using the set of simultaneous equations we solved
earlier. This is the 2 x 2 matrix:
A= [ ''1

10 30

Repeating the sequence of steps yields the determinant

which is then expanded into
I 4c; 3:! 1 = (4 -A) (30 - A) - 100 = 0

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