Write a system of linear equations represented by the augmented matrix. Then write the solution set. 1 − 2 3 − 1 0 1 4 − 11 0 0 1 − 2

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Answer 1

Textbook Question

Chapter 9, Problem 1RE

Write a system of linear equations represented by the augmented matrix. Then write the solution set.

1 − 2 3 − 1 0 1 4 − 11 0 0 1 − 2

Expert Solution & Answer

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2

Solve further as:

x−2y+3z=−1y+4z=−11z=−2

Also, solve for the solution set of the given augmented matrix as:

1−23−101411001−2

Apply operation 2R2+R1→R1 on above matrix as:

1011−2301411001−2

Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:

100−1010−3001−2

So, the solution set is −1,−3,−2 .

Therefore, the system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

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Answer 2

Textbook Question

Chapter 9, Problem 1RE

Write a system of linear equations represented by the augmented matrix. Then write the solution set.

1 − 2 3 − 1 0 1 4 − 11 0 0 1 − 2

Expert Solution & Answer

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2

Solve further as:

x−2y+3z=−1y+4z=−11z=−2

Also, solve for the solution set of the given augmented matrix as:

1−23−101411001−2

Apply operation 2R2+R1→R1 on above matrix as:

1011−2301411001−2

Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:

100−1010−3001−2

So, the solution set is −1,−3,−2 .

Therefore, the system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

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Answer 3

Textbook Question

Chapter 9, Problem 1RE

Write a system of linear equations represented by the augmented matrix. Then write the solution set.

1 − 2 3 − 1 0 1 4 − 11 0 0 1 − 2

Expert Solution & Answer

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2

Solve further as:

x−2y+3z=−1y+4z=−11z=−2

Also, solve for the solution set of the given augmented matrix as:

1−23−101411001−2

Apply operation 2R2+R1→R1 on above matrix as:

1011−2301411001−2

Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:

100−1010−3001−2

So, the solution set is −1,−3,−2 .

Therefore, the system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

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Answer 4

Textbook Question

Chapter 9, Problem 1RE

Write a system of linear equations represented by the augmented matrix. Then write the solution set.

1 − 2 3 − 1 0 1 4 − 11 0 0 1 − 2

Expert Solution & Answer

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2

Solve further as:

x−2y+3z=−1y+4z=−11z=−2

Also, solve for the solution set of the given augmented matrix as:

1−23−101411001−2

Apply operation 2R2+R1→R1 on above matrix as:

1011−2301411001−2

Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:

100−1010−3001−2

So, the solution set is −1,−3,−2 .

Therefore, the system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2

Solve further as:

x−2y+3z=−1y+4z=−11z=−2

Also, solve for the solution set of the given augmented matrix as:

1−23−101411001−2

Apply operation 2R2+R1→R1 on above matrix as:

1011−2301411001−2

Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:

100−1010−3001−2

So, the solution set is −1,−3,−2 .

Therefore, the system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Answer 8

Expert Solution & Answer

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2

Solve further as:

x−2y+3z=−1y+4z=−11z=−2

Also, solve for the solution set of the given augmented matrix as:

1−23−101411001−2

Apply operation 2R2+R1→R1 on above matrix as:

1011−2301411001−2

Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:

100−1010−3001−2

So, the solution set is −1,−3,−2 .

Therefore, the system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To calculate:The system of linear equations represented by the augmented matrix.

1−23−101411001−2

Also, write its solution set.

Answer 12

Answer to Problem 1RE

The system of linear equations represented by the given augmented matrix is:

x−2y+3z=−1y+4z=−11z=−2

And the solution set of the given augmented matrix is −1,−3,−2 .

Answer 13

Explanation of Solution

Calculation:

Consider the given augmented matrix 1−23−101411001−2 .

Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.

Then, the linear equations can be written as:

x−2y+3z=−10x+y+4z=−110x+0y+z=−2