Solving Systems Using Matrices

2x + 5y + z = -12

-x + 4y + 3z = -4

5x - 2z = -13

• x = 3, y = 1, z = 1

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1

Solve, if possible:

3x + 2y - 3z = 13

4z + 4x = 12

-2x - y + z = 8

• x = 3, y = 1, z = 1

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1

Solve, if possible:

-2x - 4y + 4z = 14

4x + 2y + 4z = -4

x + 2z = -2

• x = 3, y = 1, z = 1

• No solution

• Infinitely many solutions

• x = -3, y = -1, z = -1

Write the augmented matrix that corresponds to the system

• A

• B

• C

• D

Which of the following is the correct representation for the system of equations?

• A

• B

• C

• D

Write the following system of equations as an augmented matrix.

• 
• 
• 
• 

Jeffrey wrote a matrix to represent his system of equations. What was his mistake

• The z's are not aligned correctly

• There should be a one in the top row for zero

• There should be a zero in the second column of the third representing the y

• Nothing. This is correct.

Jemima is in the process of reducing her matrix. Her next step is shown here. What was her mistake?

• She should have multiplied the 3 by its' reciprocal

• She has the bottom row already solved for

• She multiplied her top row correctly, but that doesn't change the first row when we add it to another row

• Nothing. She performed her step correctly.

Which row command is an appropriate next step?

• 7R2 + R3 -> R3

• -7R1 + R3 -> R3

• 7R3 -> R3

• -7R2 + R3 -> R3

What is the solution to this system?

• <(2, 3, -1)>

• <(3, -1, 2)>

• <( -1, 3, 2)>

• <(2, -1, 3)>