# Proof involving linear algebra

• spoc21
In summary: If it works, then you are done with the induction.In summary, the conversation is about a problem where the objective is to use proof by induction to show that a specific set of inequalities holds for a given sequence. The problem is not clearly stated and may have a mistake. The speaker also mentions that they have solved a similar problem before.
spoc21

## Homework Statement

Hi, I'm supposed to solve the following question using proof by induction, and am very confused with it. It would be greatly appreciated if someone could help me solve this problem:

Let an = 2 and an+1$$\frac{4a_n -3}{a_n}$$ for n >=1. Show that 1$$\leq a_n \leq a_(n+1)\leq3$$ for all n $$\geq1$$
please note that _ = subscript I am very confused with this problem, and would appreciate any help.Thanks!

What you posted doesn't make sense. Check to make sure that it's written correctly.

spoc21 said:

## Homework Statement

Hi, I'm supposed to solve the following question using proof by induction, and am very confused with it. It would be greatly appreciated if someone could help me solve this problem:

Let an = 2 and an+1$$\frac{4a_n -3}{a_n}$$ for n >=1. Show that 1$$\leq a_n \leq a_(n+1)\leq3$$ for all n $$\geq1$$
please note that _ = subscript

I am very confused with this problem, and would appreciate any help.

Thanks!

I have myself solved something simular not so long a ago I think it suppose to say

Let $$a_n = 2$$

Let $$a_{n+1} = \frac{4 {a_n}-3}{a_n}$$ for $$n \geq 1$$

and then

"Show that 1$$\leq {a_n} \leq {a_{n+1}}\leq 3$$ for all $$n \geq 1$$"

I could be wrong but this setup makes me think about a socalled recurrence relation..
But you are right it looks like something is missing.

Last edited:
Have you tried anything yet? Induction has some very clear steps. First, show it is true for n=1. Then assume n=k is true and see what happens with k+1.

## 1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations and their representations in vector spaces. It involves operations such as addition, subtraction, multiplication, and division of vectors and matrices.

## 2. How is linear algebra used in proofs?

Linear algebra is used in proofs to solve systems of linear equations and to find the properties of linear transformations. It also provides a framework for analyzing the properties of vectors and matrices, which are often used in proofs involving geometric concepts.

## 3. What are the fundamental concepts in linear algebra?

The fundamental concepts in linear algebra include vector spaces, linear transformations, and matrices. Other important concepts include determinants, eigenvalues and eigenvectors, and orthogonality.

## 4. Why is linear algebra important in science?

Linear algebra is important in science because it provides a powerful tool for solving complex mathematical problems that arise in various fields such as physics, engineering, and computer science. It also helps in understanding and representing data in a more efficient and concise manner.

## 5. How can I improve my understanding of linear algebra in proofs?

To improve your understanding of linear algebra in proofs, it is important to practice solving problems and proofs involving linear algebra concepts. You can also refer to textbooks and online resources for additional explanations and examples. Additionally, seeking guidance from a math tutor or joining a study group can also be beneficial.

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