The table shows the market prices per pound that a trucker can get for his load of fruit in three cities: San Francisco, Las Vegas and Los Angeles.
S.F L.V L.A
PEACHES $0.50 $0.60 $0.40
APPLES $0.40 $0.80 $0.50
The trucker has a load of 5000 lbs. of peaches and 3000 lbs. of apples.Write the info from the table as a 2x3 matrix B.Write a row matrix A for which the entries represent the number of lbs. of each type of fruit in the truck. If C=AB, find c11.What does this entry of C represent?
how to solve tihs matrix?
To write the information from the table as a 2x3 matrix B, we need to list the market prices per pound for each fruit in each city.
The table gives us the following data:
| | San Francisco | Las Vegas | Los Angeles |
|--------|--------------|-----------|-------------|
| Peaches | $0.50 | $0.60 | $0.40 |
| Apples | $0.40 | $0.80 | $0.50 |
So the matrix B would be:
B =
| $0.50 $0.60 $0.40 |
| $0.40 $0.80 $0.50 |
To write a row matrix A representing the number of pounds of each type of fruit in the truck, we can list the number of pounds for each fruit in the order mentioned (peaches, apples). So in this case, A = [5000 3000].
To find C = AB, we need to multiply matrices A and B.
C = AB = [5000 3000] *
| $0.50 $0.60 $0.40 |
| $0.40 $0.80 $0.50 |
The result will be a 1x3 matrix.
To find c11, we need to find the first entry in the resulting matrix C. In this case, c11 represents the value of multiplying the first row of A by the first column of B. So c11 = (5000 * $0.50) + (3000 * $0.40).
The entry c11 represents the total value of the pounds of peaches in the truck at the market price in San Francisco.