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/
|
The scalar product of two three-dimensional vectors can be interpreted as the product of two matrices.
Find the scalar product of the vectors 2i + 3j - 6k and i + 0j + 9k.
/1\
(2 3 -6) * |0| = (-52)
\9/ |