Solving Systems with Augmented Matrices Lesson (2025)

Solving Systems with Augmented Matrices

Open Ended

When should you use augmented matrices?

Multiple Choice

What does rref stand for?

• Reduced Row Echelon Form

• Rally Row Extinct Form

• Rounded Row Engineering Form

• Random Reduced Emerging Form

Multiple Choice

What are you to look for in the solution matrix to know the solution is unique, an ordered pair or triple?

• the first part of the solution matrix will look like the identity matrix

• The solution matrix will be a square matrix

• One of the rows in the solution matrix will have all zeros

• One of the rows in the solution matrix will have zeros and 1 number.

Multiple Choice

What in the answer matrix indicates that there is no solution?

• The first part of the solution matrix will look like the identity matrix

• The solution matrix will be a square matrix

• One of the rows in the solution matrix will have all zeros

• One of the rows in the solution matrix will have zeros and 1 number.

Multiple Choice

What in the answer matrix indicates that there is an infinite number of solutions, infinitely many solutions?

• the first part of the solution matrix will look like the identity matrix

• The solution matrix will be a square matrix

• One of the rows in the solution matrix will have all zeros

• One of the rows in the solution matrix will have zeros and 1 number.

​Compare the three possible solutions on the next slide. Pay close attention to the zeros.

Now let's learn how to enter the augmented matrices into the calculator.​

Multiple Choice

Where is the rref function found on the calculator?

• In the matrix menu

• In the function window

• In the mode function

• in the math menu

Multiple Select

What two keystrokes get you into the matrix menu?

• 2nd

• x^-1

• alpha

• zoom

Multiple Select

What keystroke will move you to the Math list in the matrix menu?

• arrow up

• arrow right

• arrow down

• arrow left

Multiple Select

Where is rref found within the Math list in the matrix menu?

• A:

• B:

• 1:

• 8:

Multiple Choice

After you arrow right to MATH, what is the most common way to find rref?

• arrow up 5

• arrow down 2

• arrow to EDIT

Multiple Select

What two keystrokes will pull up the box for you to type in the dimensions of the augmented matrix?

• 2nd

• x^-1

• alpha

• zoom

Multiple Choice

The coefficients and the constants are all included in an augmented matrix.

• yes

• no

​Now let's do those examples again but this time we'll use our new method.

Multiple Choice

What are the numbers in the first row of the augmented matrix?

• 1 1 1 -3

• 1 -1 1

• 1 -1 1 -3

• 1 1 1 3

Multiple Choice

What are the numbers in the second row of the augmented matrix?

• 1 -1 -1 -3

• 1 -1 -1

• 1 -1 1 -3

• 1 1 1 -3

Multiple Choice

What are the numbers in the 3rd row of the augmented matrix?

• 5 5 1 -15

• 5 -5 1 -15

• 5 -5 0 -15

• 5 5 1 15

Multiple Select

Which row is included in the solution matrix?

• 1 -1 0 -3

• 0 0 1 0

• 0 0 0 0

Multiple Choice

Solve the system of equations using rref (augmented matrices): 

• Unique Solution:

  ( 2, 1, 6)

• infinitely many solutions

• No solution

Multiple Choice

Solve the system of linear equations.

• (3, 1, -5)

• (-3, 1, -1)

• infinitely many solutions

• no solution

Multiple Choice

Solve the system using matrices

• A

• B

• C

• D

Multiple Choice

Solve the system:

-4x - 5y - z = 18

-2x - 5y - 2z = 12

-2x + 5y + 2z = 4

• (4, 0, -2)
• (-4, 0, -2)
• Many Solutions
• No Solution

Fill in the Blanks

Solve the system. Write the answer as an ordered triple (no spaces)

5x - 4y + z = -18

   x + 3y + 7z = 38 

4x +2y - 6z = -38 

Multiple Choice

Solve the system:

4x + 2y -6z = 34

2x + y + 3z = 3

6x + 3y - 3z = 37

• $$\left(5,-\frac{7}{3},0\right)$$
  

• No Solution

• Infinite Solution

• $$\left(-5,\frac{7}{3},0\right)$$

Multiple Choice

Solve the system:

-3x + 3y + 6z = 4

3x + y + 2z = 3

-6x + 2y + 4z = 34

• $$\left(5,-\frac{7}{3},0\right)$$
  

• No Solution

• Infinite Solution

• $$\left(-5,\frac{7}{3},0\right)$$