Question 1166621: We went to the market to buy some fruit. We decided to buy some apples, strawberries, and oranges. If we buy 2
apples, 3 boxes of strawberry, and 4 oranges, the fruit would cost $15.30. If we buy 1 box of strawberry, 4 apples, and
2 oranges, the fruit would cost $10.90. If we buy 1 orange, 5 apples and 2 boxes of strawberry, the fruit would cost
$13.70. Use the Gaussian Elimination Method to solve for the price of each fruit
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
You won't learn anything about the Gaussian Elimination Method by having us work this problem for you.
Ten different tutors would probably use at least 8 or 9 different paths to the answer.
You need to find your own path....
Here is the original matrix (order apples, oranges, strawberries):
Your first objective is to get a 1 in row 1, column 1.
Three straightforward ways to do that would be (1) divide row 1 by 2; (2) divide row 2 by 4; (3) divide row 3 by 5.
However, all those ways would introduce fractions into the work, which will make the work harder. I personally would avoid that.
With the way I set up the original matrix, I would get my 1 in row 1, column 1 by subtracting row 2 from row 3 and making row 1 the result.
Note that if I had set up my original matrix with the three fruits in a different order, I could have gotten my 1 in row 1 column 1 simply by switching rows.
So already you see there are going to be multiple possible paths to the solution.
End of detail.... Now I will just outline the rest of the process.
(1) Use the 1 in row 1 column 1 to get 0's in column 1 of rows 2 and 3; do this by adding multiples of row 1 to each of rows 2 and 3.
(2) Get a 1 in row 2 column 2. Here you can't do it by adding rows, because that will destroy the "1 0 0" in column 1. So you have to get this 1 by dividing either the second or third row.
(3) Use the 1 in row 2 column 2 to get 0's in column 2 in rows 1 and 3; do this again by adding multiples of row 2 to rows 1 and 3.
(4) Get a 1 in row 3 column 3 by dividing row 3.
(5) Use the 1 in row 3 column 3 to get 0's in column 3 in rows 1 and 2, similar to step 3.
A final note....
It is aggravatingly easy to make a little mistake in your arithmetic, leading to a wrong solution. With my amount of experience with this process, I rarely get the right answer the first time through....
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