# Is This Equation Valid? Analyzing the RHS

• tetris11
In summary, the conversation discusses a given equation and whether it is valid or not. The equation is analyzed and it is determined that there is a grammatical error with the indices. The possibility of contractions in the notation is also considered. Ultimately, it is concluded that the equation is not possible due to the mismatched index structures.
tetris11

## Homework Statement

Is this equation valid?

Axy = BzzBxz+ CxyBxyBxy

## The Attempt at a Solution

BzzBxz = Bzxz+z (I think)

CxyBxyBxy = Jxy2xy (I think)

so Axy = Bzxz+z + Jxy2xy

My reasoning:
Since the two terms on the RHS do not share the same index structure, they cannot be added, and they do not share the same index structure with the LHS either.

So this equation is not possible, right?

The problem with the equation is the serious grammatical error with the indices.

Assuming they were filled in correctly, it would depend upon what contractions were implicit in the notation. For example, the following is meaningful:
Axy = BzyCxz + Duv Exy Fuv

I don't really follow.
How does that contract?

In your example, would Fuv contract to something like Jk
And then would Bz contract to L (no upper indices?)

Would it be valid to say DuvExyFuv would contract to something like Jkab?

Last edited:

## 1. What is the purpose of analyzing the RHS in an equation?

The RHS (right-hand side) of an equation is used to represent the output or result of a mathematical expression. By analyzing the RHS, we can determine if the equation is valid and follows the rules of mathematics.

## 2. How do you determine if an equation is valid?

To determine if an equation is valid, we must first ensure that both sides of the equation are equal. This means that the expression on the LHS (left-hand side) must be equal to the expression on the RHS. We can then simplify and solve the equation to check if the equality holds true.

## 3. What are the common mistakes made when analyzing the RHS of an equation?

One common mistake is forgetting to apply the same operations to both sides of the equation. For example, if we divide the LHS by 2, we must also divide the RHS by 2. Another mistake is not properly simplifying the expressions on both sides, leading to an incorrect solution.

## 4. Can an equation be valid if the RHS is undefined?

No, an equation cannot be valid if the RHS is undefined. This means that the equation does not have a defined solution and does not follow the rules of mathematics. It is important to check for undefined values in both the LHS and RHS when analyzing an equation.

## 5. How does analyzing the RHS help with problem-solving?

By analyzing the RHS, we can determine if the equation has a valid solution. This helps us to identify any mistakes or incorrect assumptions made in the problem-solving process. It also allows us to check our work and make sure that our solution is accurate.

Replies
1
Views
1K
• Differential Geometry
Replies
34
Views
2K
Replies
1
Views
1K
Replies
1
Views
5K
• Chemistry
Replies
10
Views
2K
Replies
7
Views
2K
• Precalculus Mathematics Homework Help
Replies
4
Views
2K
Replies
1
Views
3K