# Begining Linear Algebra Fruit and sugar problem

• Liondancer
In summary, we used the given equation and information about the sugar content of apples and oranges to relate Pablo's representation to the one in the lecture and wrote it as a matrix.
Liondancer

## Homework Statement

Pablo is a nutritionist who knows that oranges always have twice as much sugar as apples. When considering the sugar intake of schoolchildren eating a barrel of fruit, he represents the barrel like so:
sugar
fruit
(s; f)

There is a graph that has a 3/2 slope start from the origin with the sugar (s) variable on the x-axis and fruit (f) on the y axis

Find a linear transformation relating Pablo's representation to the one
Hint: Let "lambda" represent the amount of sugar in each apple.

none

## The Attempt at a Solution

I'm not sure where to start. =/ the equation is y=(3/2)x maybe i would convert it to (3/2)x-y=0 and yet up the matrix to be (3/2 -1) (x)
(y)

I'm not sure where to start =/

Hi there, as a scientist, I can help you with this problem. Let's break it down step by step:

1. The given equation is y = (3/2)x, which represents the relationship between sugar (x) and fruit (y). This is a linear equation in the form of y = mx, where m is the slope of the line.

2. In order to relate this to Pablo's representation, we need to use the given information that oranges have twice as much sugar as apples. This means that for every apple with an amount of sugar represented by "lambda", there will be two oranges with an amount of sugar represented by 2*lambda.

3. Let's use a variable "a" to represent the number of apples and "o" to represent the number of oranges. We can then write the equation for sugar as follows: s = a*lambda + o*2*lambda.

4. Now, we need to relate this to the equation given in the lecture, which is y = (3/2)x. We know that "x" represents the amount of sugar and "y" represents the amount of fruit. So, we can write the equation as y = (3/2)s.

5. Combining steps 3 and 4, we get y = (3/2)(a*lambda + o*2*lambda).

6. Simplifying this, we get y = (3/2)a*lambda + 3o*lambda.

7. Now, we can see that the slope of the line in the lecture's representation is (3/2)a and the y-intercept is 3o*lambda.

8. Finally, we can write this as a matrix in the form of [y] = [3/2a 3o] [x].

I hope this helps you understand the linear transformation between Pablo's representation and the one in the lecture. Let me know if you have any further questions.

## 1. What is the "Fruit and sugar problem" in Beginning Linear Algebra?

The "Fruit and sugar problem" is a classic problem in linear algebra that involves finding the amount of fruit and sugar needed to make a certain amount of a fruit salad. It is used to introduce the concept of systems of linear equations and how they can be solved using matrices and Gaussian elimination.

## 2. How is the "Fruit and sugar problem" solved using linear algebra?

The "Fruit and sugar problem" can be solved by setting up a system of linear equations, where each variable represents the amount of a specific type of fruit or sugar. These equations can then be represented in matrix form and solved using Gaussian elimination or other methods.

## 3. What real-life applications does the "Fruit and sugar problem" have?

The "Fruit and sugar problem" has many real-life applications, such as in cooking and baking, where ingredients need to be measured and combined in specific ratios. It can also be applied to other scenarios involving resources, such as budgeting or production planning.

## 4. Can the "Fruit and sugar problem" be solved using other methods besides linear algebra?

Yes, the "Fruit and sugar problem" can be solved using other methods, such as substitution or graphing. However, linear algebra provides a more efficient and systematic approach to solving the problem, especially when dealing with larger systems of equations.

## 5. How does the "Fruit and sugar problem" relate to other concepts in linear algebra?

The "Fruit and sugar problem" is a fundamental problem in linear algebra that introduces concepts such as matrices, systems of equations, and Gaussian elimination. It also serves as a building block for more advanced topics, such as vector spaces and linear transformations.

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