Question 15.7: Given the two matrices A = [8 4 3 4 5 6 ] and B = [ 0.8 0.3 ......
Given the two matrices
A = \begin{bmatrix}8& 4& 3 \\ 4& 5& 6\end{bmatrix} and B = \begin{bmatrix}0.8 & 0.3 & 0.1 \\ 0.5 &0.2& 0.4 \\ 0.3& 0.2& 0.1\end{bmatrix}
find the product matrix AB using an Excel spreadsheet.
(a) Enter the values of matrices A and B on a spreadsheet. For example, put the elements of A in cells (A2; C3) and the elements of B in cells (E2; G4). You can also enter labels for the matrix names in the rows of cells above.
(b) Highlight the cells where you want the calculated AB matrix to go. Since the order of A is 2 × 3 and the order of B is 3 × 3 the product matrix AB must have order 2 × 3. You therefore need to highlight a block of cells with 2 rows and 3 columns, such as (A6; C7). (c) With this cell range still highlighted, enter the formula = MMULT(A2;C3,E2;G4) or use whatever cells range applies for your matrices to be multiplied, or use mouse to mark out matrices to be multiplied with dotted lines.
(d) Hold down the CNTRL and SHIFT keys together and press ENTER (if you do not do this then the formula will not treat all the highlighted cells as part of an array, i.e. a matrix).
Your spreadsheet and the computed product matrix AB should now be as shown in Table 15.3. In the simple example above you can check the answers manually. However, once you are satisfied that you can use the Excel MMULTformula properly then you can use it for more complex examples where manual computation would be too time-consuming.
Table 15.3
| A | B | C | D | E | F | G | H | |
| 1 | Matrix | A | Matrix | B | ||||
| 2 | 8 | 4 | 3 | 0.8 | 0.3 | 0.1 | ||
| 3 | 4 | 5 | 6 | 0.5 | 0.2 | 0.4 | ||
| 4 | 0.3 | 0.2 | 0.1 | |||||
| 5 | Matrix | AB | ||||||
| 6 | 9 | 3.8 | 2.7 | |||||
| 7 | 8 | 3.4 | 3 |