Page 57 - Statistics and Data Analysis in Geology

Matrix Algebra

To find element c11 To find element c32

84"

The completed matrix multiplication has the appearance

In general, if the order of multiplication is reversed to BxA = C, a different
answer will be obtained:
[i i a1

In the operation A x B = C, the matrix B is said to be pvemultiplied by A. Similarly,
the matrix A can be said to be postmultiplied by B. This is simply a verbal way of
specifying the order of multiplication.
If two square matrices are multiplied, the product is a square matrix of the
same size. However, if an m x n matrix is multiplied by an n x r matrix, the result
is an m x r matrix. That is, the product matrix has the same number of rows
as the premultiplier matrix on the left and the same number of columns as the
postmultiplier matrix on the right. For example, premultiplying a 3 x 2 matrix by a
5 x 3 matrix results in a 5 x 2 matrix:

12 12
7 6

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