Page 83 - Excel for Scientists and Engineers: Numerical Methods

60 EXCEL: NUMERICAL METHODS

where A-' is the inverse matrix and I is the unit matrix. The process for manual
calculation of the inverse of a matrix is complicated and need not be described
here, since matrix inversion can be done conveniently using Excel's worksheet
function MINVERSE.
Evaluation of the Determinant. A determinant is a mathematical value
that can be calculated for a square matrix. Determinants are useful for the
solution of systems of simultaneous equations, as will be discussed in chapter 9.
The "pencil-and-paper" evaluation of the determinant of a matrix of N rows x N
columns is tedious, but it can be done simply by using Excel's worksheet
function MDETERM.

Excel's Built-in Matrix Functions
Performing matrix mathematics with Excel is very simple. Let's begin by
assuming that the matrices A and B have been defined by selecting the 3R x 3C
arrays of cells containing the values shown in Figure 3-1 and naming them by
using Define Name. Remember, we're simply assigning a range name to a range
of cells. We usually refer to it as a range or an array; the fact that we are calling
it a matrix simply indicates what we intend to do with it.

Figure 3-1. Ranges of cells defined as A and B.
(folder 'Chapter 03 (Matrices) Examples, workbook 'Matrix Math', sheet 'Sheet 1')

Addition or Subtraction. To add a constant (e.g., 3) to matrix A, simply
select a range of cells the same size as the matrix, enter the formula =A+3, then
press COMMAND+RETURN or CONTROL+SHIFT+FETURN (Macintosh) or
CONTROL+SHIFT+ENTER (Windows). When you "array-enter" a formula by
pressing e.g., CONTROL+SHIFT+ENTER, Excel puts braces around the formula, as
shown below:
{=A+3}