#### Question:

Find the reduced row echelon form of the following matrices and then give the solution to the system that is represented by the augmented matrix. TO 4 7 0 6. a. 2 1 0 0 Lo 3 1 - 4 6. b. 54 30 71 8 6 2 -3 4 3 2 -10]

Posted By Admin @ September 03, 2022

Find the reduced row echelon form of the following matrices and then give the solution to the system that is represented by the augmented matrix. TO 4 7 0 6. a. 2 1 0 0 Lo 3 1 - 4 6. b. 54 30 71 8 6 2 -3 4 3 2 -10]

**Answer:**

a)

Reduced Row Echelon:

Solution to the system:

b)

Reduced Row Echelon:

Solution to the system:

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

**Step-by-step explanation:**

To find the reduced row echelon form of the matrices, let's use the Gaussian-Jordan elimination process, which consists of taking the matrix and performing a series of row operations. For notation, R_i will be the transformed column, and r_i the unchanged one.

**a) **

Step by step operations:

1. Reorder the rows, interchange Row 1 with Row 2, then apply the next operations on the new rows:

Resulting matrix:

2. Set the first row to 1

Resulting matrix:

3. Write the system of equations:

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

**b)**

1.

Resulting matrix:

2. Write the system of equations:

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

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