# Linear Combination - Are these solutions wrong?

• pyroknife
Therefore, dividing row II by (b-a) may result in a division by 0, which is undefined. It would be more appropriate to consider this potential issue and handle it properly instead of blindly following the given solution.
pyroknife

I, II represent rows 1 and 2, respectively.

I am not agreeing with these solutions at step 3 of 5, where they multiply row 2 by 1/(b-a). Correct me if I'm wrong, but we do not know if b-a=0, so I do not think we can divide row II by (b-a) because of the potential of dividing by 0?

What do you guys think?

pyroknife said:

I, II represent rows 1 and 2, respectively.

I am not agreeing with these solutions at step 3 of 5, where they multiply row 2 by 1/(b-a). Correct me if I'm wrong, but we do not know if b-a=0, so I do not think we can divide row II by (b-a) because of the potential of dividing by 0?

What do you guys think?
I agree with you. From the given information, we can't say that b - a ≠ 0.

## What is a linear combination?

A linear combination is a mathematical operation that involves multiplying a set of numbers by coefficients and then adding them together. The coefficients can be any real numbers and the numbers being multiplied are typically variables or constants.

## How is a linear combination used in science?

Linear combinations are used in science to represent the relationship between variables in a system. They can be used to model physical phenomena, such as chemical reactions or fluid dynamics, and to analyze data in fields such as biology or economics.

## Why are there multiple solutions for a linear combination?

There can be multiple solutions for a linear combination because the coefficients used in the operation can vary, resulting in different combinations of the numbers being multiplied. Additionally, some systems may have infinite solutions, meaning that any value for the coefficients will result in a valid solution.

## What does it mean if a linear combination has no solution?

If a linear combination has no solution, it means that the system of equations being modeled is inconsistent or contradictory. This can occur when there are not enough equations to uniquely determine the values of the variables, or when the equations are incompatible with each other.

## How can one determine if a set of solutions for a linear combination is correct?

To determine if a set of solutions for a linear combination is correct, one can substitute the values into the original equations and see if they satisfy all of the equations. If the solutions do not satisfy all of the equations, then they are not valid solutions for the linear combination.

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