# Confusion with how to make an augmented matrix

• John004
In summary, The first row in the augmented matrix should be [ 0 -1 -1 1 | -4 ], as the "4" in the first equation is most likely a misprint.
John004

## Homework Statement

So in the attachment you'll see a picture taken from a linear algebra book where a linear system of equations is presented in the equivalent augmented matrix form. I'm confused about the representation of the first equation in the augmented matrix. What happened to the constant 4? Shouldn't the first row in the matrix be [ 0 -1 -1 1 | -4 ]?

## The Attempt at a Solution

#### Attachments

• Linear Algebra.png
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John004 said:
Shouldn't the first row in the matrix be [ 0 -1 -1 1 | -4 ]?

Yes, it should be. The "4" in the first equation is probably a misprint.

Stephen Tashi said:
Yes, it should be. The "4" in the first equation is probably a misprint.
Ah ok, good. I thought I was going crazy for a second there.

## 1. What is an augmented matrix?

An augmented matrix is a mathematical representation of a system of linear equations. It is composed of the coefficients of the variables in the equations along with an additional column representing the constants. It is used to solve systems of equations using various methods such as row reduction or Gaussian elimination.

## 2. How do I create an augmented matrix?

To create an augmented matrix, you first need to write out the equations in the system. Then, list the coefficients of each variable in the equations in a matrix format. The additional column on the right will contain the constants. Make sure each row in the matrix corresponds to the same equation as the original system.

## 3. Can I use an augmented matrix to solve any system of equations?

Yes, you can use an augmented matrix to solve any system of linear equations. However, some systems may have no solution or infinite solutions, which will be reflected in the final form of the augmented matrix.

## 4. What are the benefits of using an augmented matrix?

An augmented matrix allows for a systematic approach to solving systems of equations. It also makes it easier to perform row operations and manipulate the equations to find the solution. Additionally, it can be used to solve larger systems of equations more efficiently than solving each equation individually.

## 5. Are there any common errors when creating an augmented matrix?

One common error when creating an augmented matrix is mixing up the coefficients of the variables with the constants. It is important to keep the coefficients in the same order in each row and to not mix them up with the constants. Another error can be forgetting to add the additional column for the constants, which is necessary to create an augmented matrix.

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