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 ]

Question

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Answer 1

Textbook Question

Chapter 6, 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 [1−23−1014−11001−2] and the solution set.

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]

Thus, x=−1,y=−3 and z=−2.

Therefore, the solution set is {(−1,−3,−2)}.

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Answer 2

Textbook Question

Chapter 6, 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 [1−23−1014−11001−2] and the solution set.

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]

Thus, x=−1,y=−3 and z=−2.

Therefore, the solution set is {(−1,−3,−2)}.

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Answer 3

Textbook Question

Chapter 6, 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 [1−23−1014−11001−2] and the solution set.

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]

Thus, x=−1,y=−3 and z=−2.

Therefore, the solution set is {(−1,−3,−2)}.

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Answer 4

Textbook Question

Chapter 6, 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 [1−23−1014−11001−2] and the solution set.

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]

Thus, x=−1,y=−3 and z=−2.

Therefore, the solution set 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 [1−23−1014−11001−2] and the solution set.

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]

Thus, x=−1,y=−3 and z=−2.

Therefore, the solution set is {(−1,−3,−2)}.

Answer 8

Expert Solution & Answer

To determine

To calculate: The system of linear equations represented by the augmented matrix [1−23−1014−11001−2] and the solution set.

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]

Thus, x=−1,y=−3 and z=−2.

Therefore, the solution set 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 [1−23−1014−11001−2] and the solution set.

Answer 12

Answer to Problem 1RE

Solution:

The system of linear equations is x−2y+3z=−1y−4z=−11z=−2 and the solution set is {(−1,−3,−2)}.

Answer 13

Explanation of Solution

Given information:

The augmented matrix

[1−23−1014−11001−2]

Calculation:

Consider the provided augmented matrix:

[1−23−1014−11001−2]

Now, the vertical bar within the augmented matrix separates the coefficients of the variable terms in the equations from the constant terms.

Now, extract equations from the matrix as:

x−2y+3z=−10x+y−4z=−110x+0y+z=−2

Thus,

x−2y+3z=−1y−4z=−11z=−2

Now, to determine the solution set of the equations through the provided matrix, reduce the matrix into row-echelon form by performing row operations as:

[1−23−1014−11001−2]→2R2+R1→R1[1011−23014−11001−2]→−11R3+R1→R1−4R3+R2→R2[100−1010−3001−2]