# Verifying Solution for |1 -1| = P |-2 1|

• Cafka
In summary, the conversation is about verifying a solution for P^-1, with one person getting a different answer from their solutions manual and the other suggesting to check by multiplying the matrices together. The first person confirms that their answer is correct after doing the suggested check.

#### Cafka

Can someone verify this:

|1 -1| = P
|-2 1|

|-1 -1| For P^-1, i got this.
|-2 -1|

|-1 -2| My solutions manual, says this is the answer.
|-1 -1|

My solutions manual has been wrong before. The way i got my answer was to put the identity matrix to the right of P and solve for the right side and get the left into the identity.

|1 -1|1 0| = P
|-2 1|0 1|

|1 0|-1 -1| = P^-1
|0 1|-2 -1|

Thanks

A good way to check your work is to multiply the two matrices together (P, and what you get for P^-1) and check if you get the identity back.

If you do for your matrix and not that in the answer book, you can be confident you did it right.

Hurkyl said:
A good way to check your work is to multiply the two matrices together (P, and what you get for P^-1) and check if you get the identity back.

If you do for your matrix and not that in the answer book, you can be confident you did it right.
Yeah, i multiplied them back and they went ot the identity matrix.

## 1. What does "Verifying Solution" mean?

Verifying solution refers to the process of checking whether a given set of values or equations satisfies a particular condition or problem. In this case, we are checking if the values of |1 -1| and |-2 1| satisfy the equation |1 -1| = P |-2 1|.

## 2. What are the steps to verify the solution for |1 -1| = P |-2 1|?

The steps to verify the solution for |1 -1| = P |-2 1| are as follows:
1. Substitute the given values of |1 -1| and |-2 1| into the equation
2. Simplify both sides of the equation using basic arithmetic operations
3. Check if the simplified equations on both sides are equal
4. If the equations are equal, then the given values satisfy the equation and the solution is verified. If not, the solution is not valid.

## 3. What is the value of P in the equation |1 -1| = P |-2 1|?

The value of P in the equation |1 -1| = P |-2 1| is not specified. We are verifying the solution for all possible values of P. In other words, we are checking if the given values of |1 -1| and |-2 1| satisfy the equation for any value of P.

## 4. Can the solution for |1 -1| = P |-2 1| be verified using a calculator?

Yes, the solution for |1 -1| = P |-2 1| can be verified using a calculator. You can substitute the given values into the equation and use the calculator to simplify and compare the equations on both sides. However, it is always recommended to show your work and steps in paper to ensure accuracy and understanding.

## 5. Why is it important to verify solutions in science?

Verifying solutions is important in science because it ensures the accuracy and validity of our results or findings. Science is based on evidence and reproducibility, and verifying solutions helps to ensure that our experiments and calculations are performed correctly and produce reliable results. It also allows for the identification and correction of any errors or mistakes that may have been made in the process.