Page 53 - Statistics and Data Analysis in Geology

Matrix Algebra

indicated by I:

Elementary Matrix Operations

Addition and subtraction of matrices obey the rules of algebra of ordinary numbers,
with one important additional characteristic. The two matrices being added or
subtracted must be of the same order; that is, they must have the same number of
rows and columns.
To perform the operation C = A + B, every element of A is added to its cor-
responding element in B. If the matrices are not of the same order, there will be
leftover elements, and the operation cannot be completed. Subtraction, such as C
= A - B, proceeds in exactly the same manner, with every element of B subtracted
from its corresponding element in A.

Table 3-1. Bentonite production in Wyoming, 1964.
Clay (100,000 tons)
District Drilling Mud Foundry Clay Miscellaneous
Eastern 105 63 5
Montana Border 218 80 2
Central 220 76 1

As an illustration, Table 3-1 contains 1964 production figures for bentonite
from three mining districts in Wyoming. Three major grades of clay were produced:
clay for drilling mud; foundry clay; and a miscellaneous category that includes cattle
feed binder, drug and cosmetic uses, and pottery clay. These data can be expressed
[ ;: :I
in a 3 x 3 matrix, A:

A= 218 80 2

Production figures for the following year may be expressed in the same manner,
giving the matrix B:
[ :: 4"]
B= 240 121 1
3::
Total production for the 2 years in the three districts is the sum, C, of the the
matrices A and B:

84 102 4 189 165 9
218 80 2 + 240 121 1 = 458 201 3
[ i:: :: :] [ 302 28 O] [ 522 104 l]

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