Solving Systems of Equations with Augmented Matrices

This lesson demonstrates how to solve a system of three equations with three unknowns using an augmented matrix. It covers writing equations in standard form, setting up the matrix, and using the Desmos matrix calculator to find the reduced row echelon form. The solution is interpreted as an ordered triple, and the system is classified as consistent and independent.

What is the primary method used in this lesson to solve a system of equations?

• Elimination method

• Augmented matrix method

• Substitution method

• Graphical method

In the standard form of equations, where should the constants be placed?

• On the left side

• On the right side

• In the middle

• Above the variables

How many columns does a 3x4 augmented matrix have?

• 4

• 5

• 3

• 6

What is the coefficient of x in the second equation?

• 1

• 2

• -1

• 0

Which tool is used to enter the augmented matrix and find its reduced row echelon form?

• Excel

• Google Sheets

• Python

• Desmos matrix calculator

What is the first step in using the Desmos matrix calculator for this lesson?

• Click 'New Matrix'

• Enter the solution

• Solve the equations

• Graph the matrix

What does the first row of the reduced row echelon form represent?

• y = -2

• z = 1

• x = -3

• x = 1

What is the solution to the system of equations in this lesson?

• (3, 2, -1)

• (-3, -2, 1)

• (-1, -2, -3)

• (1, 2, 3)

How is the system classified when it has one solution?

• Overdetermined

• Dependent

• Inconsistent

• Consistent and independent

What does the third row of the reduced row echelon form indicate?

• z = -1

• z = 1

• y = 0

• x = 0