Find the augmented matrix for each of the following systems of linear equations:

(a)
3x1 − 2x2 = −1
4x1 + 5x2 = 3
7x1 + 3x2 = 2
(b)
2x1 + 2x3 =1
3x1 − x2 + 4 x3 = 7
6x1 + x2 − x3 = 0
(c)
x1 + 2x2 − x4 + x5 =1
3x2 + x3 − x5 = 2
x3 + 7x4 =1
(d)
x1 =1
x2 = 2
x3 = 3

What's the problem? You have all the coefficients and constants. Just write them down as an array. Just copy what you have, throwing all the variable names away, aligning the numbers in columns.

For example, #c is

1 2 0 -1 1 | 1
0 3 1 0 -1 | 2
0 0 1 7 0 | 1

(a) The augmented matrix for the system of linear equations is:

```
[ 3 -2 -1 ]
[ 4 5 3 ]
[ 7 3 2 ]
```

(b) The augmented matrix for the system of linear equations is:
```
[ 2 0 2 1 ]
[ 3 -1 4 7 ]
[ 6 1 -1 0 ]
```

(c) The augmented matrix for the system of linear equations is:
```
[ 1 2 0 -1 1 ]
[ 0 3 1 0 -2 ]
[ 0 0 1 7 0 ]
```

(d) The augmented matrix for the system of linear equations is:
```
[ 1 0 0 1 ]
[ 0 1 0 2 ]
[ 0 0 1 3 ]
```

To find the augmented matrix for each system of linear equations, we can write the coefficients of the variables and the constants in a matrix form.

(a) For the system of linear equations:
3x1 − 2x2 = −1
4x1 + 5x2 = 3
7x1 + 3x2 = 2

We can write it in matrix form as:

| 3 -2 | -1 |
| 4 5 | 3 |
| 7 3 | 2 |

The augmented matrix for this system is the matrix on the left-hand side of the equation, augmented by the matrix on the right-hand side.

(b) For the system of linear equations:
2x1 + 2x3 = 1
3x1 − x2 + 4x3 = 7
6x1 + x2 − x3 = 0

We can write it in matrix form as:

| 2 0 2 | 1 |
| 3 -1 4 | 7 |
| 6 1 -1 | 0 |

The augmented matrix for this system is the matrix on the left-hand side of the equation, augmented by the matrix on the right-hand side.

(c) For the system of linear equations:
x1 + 2x2 - x4 + x5 = 1
3x2 + x3 - x5 = 2
x3 + 7x4 = 1

We can write it in matrix form as:

| 1 2 0 -1 1 | 1 |
| 0 3 1 0 -1 | 2 |
| 0 0 1 7 0 | 1 |

The augmented matrix for this system is the matrix on the left-hand side of the equation, augmented by the matrix on the right-hand side.

(d) For the system of linear equations:
x1 = 1
x2 = 2
x3 = 3

We can write it in matrix form as:

| 1 0 0 | 1 |
| 0 1 0 | 2 |
| 0 0 1 | 3 |

The augmented matrix for this system is the matrix on the left-hand side of the equation, augmented by the matrix on the right-hand side.

I hope this explanation helps you understand how to find the augmented matrix for a system of linear equations. Let me know if you have any further questions!