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.