2,3,   1,-5,    6,5
-3,4,2,7,    1,-2,5,4


/ 1 2 \ * /1 1\  ≠  / 1 1 \ * /1 2\ 
\ 3 0 /   \0 1/     \ 0 1 /   \3 0/

1,2,  3,0  (2*2)     1,1,  0,1  (2*2)
1,1,  0,1  (2*2)     1,2,  3,0  (2*2)
1     3              4     2
3     3              3     0

/1   3 -5\   /1 0 0\   /1   3 -5\
|2  -1  8| * |0 1 0| = |2  -1  8|
\0.5 4  1/   \0 0 1/   \0.5 4  1/ 

1,3,-5,   2,-1,8,  0.5,4,1  (3*3)
1,0, 0,   0, 1,0,   0, 0,1  (3*3)
1       3    -5
2      -1     8
0.5     4     1

Fat (lipids) contains 9.3 kilocalories per gram (kcal/g), while carbohydrate (sugar) or protein contains approximately 4.1 kcal/g.  Table A indicates the percentage (the number of grams per 100 grams of substance) of proteins, fats and carbohydrates (1st, 2nd, 3rd column) of  bread, shrimps and mayonnaise  that a company uses to produce sandwiches.
How many kilocalories are provided by 1 hg of each substance?
The company wants to combine the ingredients to produce sandwiches that each contain 12 g of protein, 15 g of fat and 40 g of carbohydrates. How many kilocalories are provided by 1 sandwich?

8, 1, 55,   14, 1, 3,   1, 80, 3
4.1, 9.3, 4.1
12, 15, 90

    /8   1  55\
A = |14  1   3| 
    \1  80   3/

/8   1  55\   /4.1\   /267.6\   /270\
|14  1   3| * |9.3| = | 79  | = | 80|   (round)
\1  80   3/   \4.1/   \760.4/   \760/

   kcal provided by 1 hg of each substance

             /4.1\
(12 15 90) * |9.3| = (352.7) = (350)
             \4.1/

       kcal provided by 1 sandwich

1,1,1,   0,1,1,   0,0,1
1,1,1,   0,1,1,   0,0,1

/1 1 1\   /1 1 1\   /1 2 3\
|0 1 1| * |0 1 1| = |0 1 2| 
\0 0 1/   \0 0 1/   \0 0 1/

1,2,3,4,  0,1,2,3,  0,0,1,2,  0,0,0,1  (4*4)
1,-2,1,0, 0,1,-2,1, 0,0,1,-2, 0,0,0,1  (4*4)

1     0     0     0
0     1     0     0
0     0     1     0
0     0     0     1

/1 2 3 4\   /1 -2  1  0\   /1 0 0 0\
|0 1 2 3| * |0  1 -2  1| = |0 1 0 0|
|0 0 1 2|   |0  0  1 -2|   |0 0 1 0|
\0 0 0 1/   \0  0  0  1/   \0 0 0 1/