Solving Systems of Equations with Augmented Matrices

This video tutorial demonstrates how to solve a system of three equations with three unknowns using an augmented matrix. It guides viewers through forming the matrix, entering it into a TI-84 calculator, and using reduced row echelon form to find the solution. The tutorial emphasizes the importance of correctly entering matrix elements and interpreting the solution as an ordered triple, classifying the system as consistent and independent.

What is the primary tool used in this video to solve the system of equations?

• TI-84 Graphing Calculator

• TI-89 Graphing Calculator

• Casio Graphing Calculator

• HP Graphing Calculator

In forming the augmented matrix, where should the constants be placed?

• Third column

• Second column

• First column

• Fourth column

What is the coefficient of x in the second equation of the example?

• -1

• 2

• 0

• 1

How many rows and columns does the augmented matrix have in this example?

• 3 rows and 3 columns

• 4 rows and 4 columns

• 3 rows and 4 columns

• 4 rows and 3 columns

What is the first step after entering the matrix into the TI-84 calculator?

• Solve the equations

• Check the entries

• Convert to reduced row echelon form

• Graph the equations

Which function is used on the TI-84 to convert the matrix to reduced row echelon form?

• det

• rref

• inv

• ref

What does the first row of the reduced row echelon form represent in terms of the variables?

• x = -3

• y = -2

• z = 1

• x = 2

What is the solution to the system of equations in the form of an ordered triple?

• (3, 2, -1)

• (-1, -2, 3)

• (1, 2, 3)

• (-3, -2, 1)

How is the system classified when there is exactly one solution?

• Inconsistent and dependent

• Consistent and independent

• Consistent and dependent

• Inconsistent and independent

What is the equivalent equation for the third row in the reduced row echelon form?

• x = 1

• y = -2

• z = 1

• x = -3