Sullivan Algebra and Trigonometry: Section 12.3 Objectives of this Section Write the Augmented Matrix of a System of Linear Equations Write the System from the Augmented Matrix Solve Systems of Linear Equations Using Matrices

Augmented Matrix:

Row Operations on an Augmented Matrix 1. Interchange any two rows. 2. Replace a row by a nonzero multiple of that row. 3. Replace a row by the sum of that row and a constant multiple of some other row.

Echelon Form of an Augmented Matrix

Solve the following system of equations: First, write the system as an augmented matrix. Then, use row operations to write the matrix in row echelon form

Let z = 5 in (2):Let y = -2, z = 5 in (1): Solution: x = 1, y = -2, z = 5

Using row operations, the system can be written as an augmented matrix in row echelon form, similar to the previous example resulting in: Dependent system: Infinitely many solutions

Using row operations, the system can be written as an augmented matrix in row echelon form, similar to the previous example resulting in: The system is inconsistent. No solution.