1. 3-6 Solving Systems
Using Matrices
Algebra II Unit 3 Linear Systems
© Tentinger

2. Essential Understanding and
Objectives
• Essential Understanding: You can use a Matrix to represent and
solve a system of equations without writing the variables.
• Objectives:
• Students will be able to:
• Represent a system of linear equations with a matrix
• Solve a system of equations using matrices

3. Iowa Core Curriculum
• Algebra
• A.REI.8 (+) Represent a system of linear equations as a single
matrix equation in a vector variable.

4. Matrix
• Matrix: a rectangular array of numbers. Displayed with
brackets and the dimensions are the number of rows by the
number of columns.
• Dimensions: 2x3
• Matrix Element: each number in the matrix. Represented by
its row and column number as a subscript. For example in
matrix A, a12 is the element in row 1 column 2 and is the
fourth element.

5. Identify a Matrix Element.
• A=
• What is element a23 in matrix A?
• What is element a13 in Matrix A
• What is element a33 in matrix A?
• What is element a24 in matrix A?

6. Representing a system of
equations with a matrix.
• Each row represents an equation
• Each column represents a variable, except the last column
• The last column shows the constants to the right of the equal
signs.
• You only write the constant with the variable in the matrix
• Draw a vertical bar to replace the equal signs
• System Matrix

7. How can you represent the system
of equations with a matrix?

8. What linear system of equations
does the matrix represent?

9. Solving Systems
• To solve a system of equations using matrices it should look
like this when finished row reducing:
• where
x=a
y=b
z=c

10. Row operations:
• Switch any two rows:
Becomes
• Multiply a row by a constant:
Becomes
• Add one row to another:
Becomes
• Combine any of these steps
• Matrices that represent the solution of a system are in
Reduced Row Echelon Form

11. Solving a system using a
matrix
• What is the solution of the system?

12. On the Calculator
• Matrices that represent the solution of a system are in
Reduced Row Echelon Form
• Graphing Calculators will do the work for you using the rref
function.
• On the Calculator
• Enter in the system into the matrix
• Apply the rref() function to the matrix
• List the solutions
• What is the solution of the system of equations?

13. Homework
• Pg 179-180
• #8-14, 18 – 20, 24-26, 30, 34, 38
• 15 problems