# FC 170 - Matrix Multiplication

The matrix multiplication function code multiplies a pair of three-by-three matrices. The output is a three-by-three matrix. Like matrix addition (function code 169), use matrix multiplication for system modeling and simulation. The outputs show the effects of various values of several different parameters.

Matrix multiplication can implement advanced control strategies that incorporate several independent variables. Outputs:

 Blk Type Description N R Product (A11 x B11) + (A12 x B21) + (A13 x B31) or ( x ) + ( x ) + ( x ) N+1 R Product (A11 x B12) + (A12 x B22) + (A13 x B32) or ( x ) + ( x ) + ( x ) N+2 R Product (A11 x B13) + (A12 x B23) + (A13 x B33) or ( x ) + ( x ) + ( x ) N+3 R Product (A21 x B11) + (A22 x B21) + (A23 x B31) or ( x ) + ( x ) + ( x ) N+4 R Product (A11 x B12) + (A22 x B22) + (A23 x B32) or ( x ) + ( x ) + ( x ) N+5 R Product (A21 x B13) + (A22 x B23) + (A23 x B33) or ( x ) + ( x ) + ( x ) N+6 R Product (A31 x B11) + (A32 x B21) + (A33 x B31) or ( x ) + ( x ) + ( x ) N+7 R Product (A31 x B12) + (A32 x B22) + (A33 x B32) or ( x ) + ( x ) + ( x ) N+8 R Product (A31 x B13) + (A32 x B23) + (A33 x B33) or ( x ) + ( x ) + ( x )

Specifications:

NOTES:

1. Maximum values are:9,998 for the BRC-100, IMMFP11/12 and 31,998 for the HAC

170.1   Explanation

The matrix multiplication function code multiplies two three-by-three matrices to form a three-by-three matrix of real values.  Matrices multiply row by column. To form the first row of the product matrix, row one of matrix A multiplies by columns one, two and three of matrix B. The second and third rows of the product matrix form similarly. Row two of matrix A multiplies by columns one, two and three of matrix B to form the second row of the product matrix and row three of matrix A multiplies by columns one, two and three of matrix B to form the last row of the product matrix.

The row by column multiplication sums the products of the like elements to get one value. The first value in row one of matrix A multiplies by the first value in column one of matrix B. That product adds to the products of the second and third values to produce the value in the product matrix as Figure 170-1 shows. 