The second one is easier if we identify what the parts of each martix represent
The first matrix
S M L
[ 1.50 2.50 6.50 ] prices of the three sizes at store 1
[ 2.00 3.50 8.00 ] prices of the three sizes at store 2
The second matrix
No. on shelf No. in stockroom
of each size of each size
10 24 S
18 48 M
6 12 L
The first row of the first matrix x the first column of the second gives the total price of the stock on the shelves in store 1....so this is entry a11 in the resulting matrix =
(1.50)(10 ) + (2.50)*(18) + (6.50)(6) = 99
The first row of th first matrix x the secolumn of the second matrix gives the total price of the stock in the stockroom at store 1....this is entry a12 in the resulting matrix =
(1.50)(24 ) + (2.50)(48) + (6.50)(12) = 234
The second row of the first matrix x the first column of the second matrix gives the total price of the stock on the shelves at store 2......this is entry a21 in the resulting matrix =
(2.00)(10) + (3.50)(18) + (8.00)(6) = 131
Finally.....second row of the first matrix x second column of the second matrix gives the total price of the stock in the stockroom of store 2.....this is entry a22 in the resulting matrix =
(2.00)(24) + (3.50)(48) + (8.00)(12) = 312
So we have the following resultant (product) matrix :
Shelves Stockroom
99 234 Store 1
131 312 Store 2
The rows represent the different stores
And the columns represent the location of the stock within each store
