Use matrices as a tool to solve a system of three equations with three unknowns.

• Find and interpret the reduced row-echelon answer matrix for the solution to the system of three equations with three unknowns
• Interpret a consistent and independent system of three equations with three unknowns resulting in an intersection point
• Interpret a consistent and dependent system of three equations with three unknowns resulting in an intersection line
• Interpret an inconsistent system of three equations with three unknowns resulting in no common intersections

• Augmented matrix
• Reduced row-echelon form
• Main diagonal
• Consistent system of equations
• Inconsistent system of equations
• Dependent system of equations
• Independent system of equations

This lesson involves using matrices as a tool to solve a system of three equations with three unknowns. As a result, students will:

• Enter the coefficients of a system into an augmented matrix.
• Find the reduced row-echelon form of the matrix using the rref( ) command on the TI-Nspire.
• Translate the answer matrix into a solution of the system, both algebraically and geometrically.