**Solve the Linear System Using Elementary Row Operations**Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system.\[\begin{pmatrix}1 & -5 & 5 & 0 & -1 \\0 & 2 & -7 & 0 & 5 \\0 & 0 & 1 & 4 & -4 \\0 & 0 & 2 & 6 & 0\end{pmatrix}\]**Question:**What should be the first elementary row operation performed? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.- A. Replace row 2 by its sum with  times row 4. (Type an integer or a simplified fraction.)- B. Interchange row 3 and row 2.- C. Replace row 4 by its sum with  times row 3. (Type an integer or a simplified fraction.)- D. Scale row 1 by . (Type an integer or a simplified fraction.)**Explanation:**To solve the linear system using elementary row operations, we can proceed with one of the following steps:1. **Interchange Rows (i.e., Swapping Two Rows):** This operation is often useful to get a nonzero entry in a leading position. 2. **Scaling a Row:** Multiplying a row by a nonzero scalar to change the coefficient of a particular variable.3. **Replacement (i.e., Adding/Subtracting Rows):** This involves replacing one row with the sum of itself and a multiple of another row. It is used to introduce zeros below the pivot position.In this specific problem:- We aim to create an identity matrix on the left side of the augmented matrix to simplify the solution process. Carefully consider the interchanging, scaling, and replacement operations needed in this scenario to progress towards the identity matrix form and facilitate solving the linear system.

Given matrix is not in Echelon form.So, first we need to change it in echelon form. We can see first…

Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next 1 - 5 50 -1 two elementary row operations that should be performed in the process of solving the system. 2 -7 0 1 4 - 4 2 6 What should be the first elementary row operation performed? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Replace row 2 by its sum with times row 4. (Type an integer or a simplified fraction.) OB. Interchange row 3 and row 2. O C. Replace row 4 by its sum with times row 3. (Type an integer or a simplified fraction.) O D. Scale row 1 by o O

Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next 1 - 5 50 -1 two elementary row operations that should be performed in the process of solving the system. 2 -7 0 1 4 - 4 2 6 What should be the first elementary row operation performed? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Replace row 2 by its sum with times row 4. (Type an integer or a simplified fraction.) OB. Interchange row 3 and row 2. O C. Replace row 4 by its sum with times row 3. (Type an integer or a simplified fraction.) O D. Scale row 1 by o O

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A: Topic:- matrix

Question

**Solve the Linear System Using Elementary Row Operations**

Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system.

\[
\begin{pmatrix}
1 & -5 & 5 & 0 & -1 \\
0 & 2 & -7 & 0 & 5 \\
0 & 0 & 1 & 4 & -4 \\
0 & 0 & 2 & 6 & 0
\end{pmatrix}
\]

**Question:**
What should be the first elementary row operation performed? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- A. Replace row 2 by its sum with  times row 4.

(Type an integer or a simplified fraction.)

- B. Interchange row 3 and row 2.

- C. Replace row 4 by its sum with  times row 3.

(Type an integer or a simplified fraction.)

- D. Scale row 1 by .

(Type an integer or a simplified fraction.)

**Explanation:**

To solve the linear system using elementary row operations, we can proceed with one of the following steps:

1. **Interchange Rows (i.e., Swapping Two Rows):** This operation is often useful to get a nonzero entry in a leading position.

2. **Scaling a Row:** Multiplying a row by a nonzero scalar to change the coefficient of a particular variable.

3. **Replacement (i.e., Adding/Subtracting Rows):** This involves replacing one row with the sum of itself and a multiple of another row. It is used to introduce zeros below the pivot position.

In this specific problem:
- We aim to create an identity matrix on the left side of the augmented matrix to simplify the solution process.

Carefully consider the interchanging, scaling, and replacement operations needed in this scenario to progress towards the identity matrix form and facilitate solving the linear system.

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