Complete the reduced row echelon form for the matrix shown.

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.