Page 85 - Excel for Scientists and Engineers: Numerical Methods

62 EXCEL: NUMERICAL METHODS

Figure 3-5. Result matrix B.A.
(folder 'Chapter 03 (Matrices) Examples, workbook 'Matrix Math', sheet 'Sheet 1')

Matrix multiplication of two matrices is possible only if the matrices are
conformable, that is, if the number of columns of A is equal to the number of
rows of B. The opposite condition, if the number of rows of A is equal to the
number of columns of B, is not equivalent. The following examples, involving
multiplication of a matrix and a vector, illustrate the possibilities:
MMULT (4 x 3 matrix, 3 x 1 vector) = 3 x 1 result vector
MMULT (4 x 3 matrix, 1 x 4 vector) =#VALUE!

MMULT (1 x 4 vector, 4 x 3 matrix) = 1 x 4 result vector
In other words, the two inner indices must be the same.
Transposition. The transpose of a matrix may be calculated by using the
worksheet function TRANSPOSE(array) or obtained manually by using the
Transpose option in the Paste Special.. . menu command.
The size of the array that can be transposed is limited only by the size of the
Excel spreadsheet; the number of rows or columns cannot be greater than 256.
Matrix Inversion. The process for inverting a matrix "manually" (i.e., using
pencil, paper and calculator) is complicated, but the operation can be carried out
readily by using Excel's worksheet function MINVERSE(array). The inverse of
the matrix B above is shown in Figure 3-6.

Figure 3-6. Result matrix B-'.
(folder 'Chapter 03 (Matrices) Examples, workbook 'Matrix Math', sheet 'Sheet1 ')

The size of the matrix must not exceed 52 rows by 52 columns.

Evaluation of the Determinant. The determinant of a matrix of Nrows x
N columns can be obtained by using the worksheet function MDETERM(array).