442 Chapter 14 Electronic Spreadsheets
Here, matrix [N] is a three by three (or 3 3) matrix whose elements are numbers, and {L}is
a three by one matrix with its elements representing variablesx,y,andz. The [N] is called a
square matrix. Asquarematrix has the same number of rows and columns. The element of a
matrix is denoted by its location. For example, the element in the first row and the third col-
umn of matrix [N] is denoted byn 13 , which has a value of nine. In this book, we denote the
matrix by aboldface letterin brackets [ ] and { }, for example: [N], [T], {F}, and the elements
of matrices are represented by regular lower case letters. The { } are used to distinguish a column
matrix. A column matrix is defined as a matrix that has one column but could have many rows.
On the other hand, a row matrix is a matrix that has one row but could have many columns.are examples of column matrices, whereas
are examples of row matrices.
In Section 18.5, we will discuss matrix algebra in more detail. If you do not have an ade-
quate background in matrix algebra, you may want to read Section 18.5 before studying the fol-
lowing examples.Matrix Algebra
Using Example 14.8, we will show how to use Excel to perform certain matrix operations.
Example 14.8 Given matrices: use
Excel to perform the following operations.
(a)
(b)
(c)
(d)If you do not have any background in matrix algebra, you may want to study Section 18.5
to learn about matrix operation rules. The manual hand calculations for this example problem
are also shown in that section.
Refer to the Excel sheets shown in the accompanying figures when following the
steps.3 A 45 C 6 ?
3 A 43 B 4 ?
3 A 4 3 B 4 ?
3 A 4 3 B 4 ?
3 A 4 £
050
837
9 29
§, 3 B 4 £
46 2
72 3
13 4
§, and 5 C 6 •
1
2
5
¶,
3 C 4 35 0 2 34 and 3 Y 4 3 y 1 y 2 y 34
5 A 6 μ
1
5
2
3
∂ and 5 X 6 •
x 1
x 2
x 3
¶
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