Use matrix methods to solve the problem.

120,000 gallons of fuel are to be divided between two airlines. Triple A Airways requires three times as much as Unity Air. How much fuel should be allocated to Triple A?
______ gal

ah ha, you did not say you know linear algebra before. In the earlier problem the determinant of your coefficient matrix was zero, no solutions.

a + u = 120,000
a - 3 u = 0

| 1 +1 | 120,000
| 1 -3 | 0

det coef matrix = -3 - 1 = -4

put right column in for a column to solve for a

| 120,000 +1 |
| 0000000 -3 | all divided by -4

-360,000/-4 = 90,000 for Triple A
then of course Unity gets 30,000

lo and behold, they add up to 120,000

thank you

To solve this problem using matrix methods, we can set up a system of equations. Let's define the following variables:

Let x represent the amount of fuel allocated to Unity Air.
Let 3x represent the amount of fuel allocated to Triple A Airways.

According to the problem statement, the total amount of fuel is 120,000 gallons. Therefore, we can write the first equation as:

x + 3x = 120,000

Combining like terms on the left side gives:

4x = 120,000

To solve for x, divide both sides of the equation by 4:

x = 120,000 / 4

Now, we can calculate x:

x = 30,000

To find the amount of fuel allocated to Triple A Airways, we can substitute the value of x into the equation for Triple A's fuel allocation:

3x = 3 * 30,000 = 90,000

Therefore, the amount of fuel to be allocated to Triple A Airways is 90,000 gallons.