Teacher Candidate: Jan Drabek
Date: February 11, 2011
Cooperating Teacher: Mike Comiskey
Grade: 9-12
School District: Seattle
School: Nathan Hale
University Supervisor: Andrea Escame-Hedger
Unit/Subject: Algebra 2
# of periods: 3
Lesson Title/Focus: Review matrix operations and system of three equations.
Learning Target
What: convert systems of equations to matrices and solve using the inverse matrix.
Standard supported by Learning Target:
A2.1.B Solve problems that can be represented by systems of equations and inequalities.
(6.5-6.6)
A2.7.A Solve systems of three equations with three variables.
Chapter 6.3 introduces solving systems with inverse matrices on pages 335-344.
How: Review homework and guided practice with a review worksheets.
Why: To enable students to build a mastery of matrices so that they can solve real world
problems involving systems of equations through the simplicity of matrices and technology.
Warm-up:
Anticipatory Set: With the fundamentals of matrix operations under our belt we are in a position
to use these operations to solve systems of equations using matrices.
The Launch/Hook: By the end of today’s lesson you will have a way to solve systems of
equations on your calculator, while we still want you to be able to solve systems through
substitution and elimination you now have a way to check your answer and find your simple
errors.
Direct Instruction, Instructional Plan, and Strategies: have students take notes on lecture
drawing parallels between using the inverse to solve Algebra equations and using the inverse to
solve matrix equations using the identity in each case (same as worksheet). Be sure to identify:
 Coefficient Matrix
 Variable Matrix
 Constant Matrix (the answer)
Learning Experiences: repeatedly refer back to the roles of the inverse, identify and variables in
a regular matrix equation have students draw parallels between these and the analogues in matrix
equations.
Guided Practice: After having students take notes have them work out the steps in pairs on the
Solving Matrix Equations WS.
Homework review: Review Back and Forth WS from last ten minutes of Quiz day.
Student Grouping: pairs.
Activity Timing: period.
Assigned Homework (which relates to the learning target): No homework.
Attachments: Solving Matrix Equations.
Reflections: This was difficult for many students to grasp, the identifying of elements in the
algebra solution was a new way of looking at things for many of them and may not have made
the steps of matrix solutions involving the inverse clear.
Attachment: WS Solving Matrix Equations.
Matrix Equation:
AX   B
Example:
 4 1  x  15 
 3 8  y   50

   
Constant Matrix
Coefficient Matrix
Variable Matrix
In this activity you will be looking at connections between solving a linear equation and solving a matrix
equation. You will be asked to explain various steps that were taken to solve the linear equation 5x = 10
Step 1:
Mathematical Steps
Explanation of steps
5x  10
This is the original equation
Explain what was done in step 2 and WHY. How does 1/5 relate
to the original equation?
Step 2:
Step 3:
1
1

5
x

 
   10
5
5
1
1  x     10
5
Where did the 1 come from in step 3? What is 1 called?
Step 4:
x2
Where did the 1 go in step 4?
Solve the given matrix equation using the inverse of the coefficient matrix. Show all the same
mathematical steps as shown in the 5x = 10 example. Include an explanation of each step in the righthand column.
 2 5  x   9 
1 3  y   4

   
Inverse of Coefficient Matrix =
 3  5
 1 2 


Mathematical Steps
Explanation of steps
Rewrite each system in matrix form and solve by using the inverse matrix. For the 2 by 2 systems show
your mathematical steps the same way you did on side one of this worksheet. Check your solutions.
a.)
2x  3y  1
 3x  4 y  0
b.)
2x  3y  1
5x  7 y  3
c.)
3x  7 y  15
4 x  9 y  19
d.)
 2x  6 y  1
5 x  15 y  2.5
a  b  c  d  e  f  30
2a  3b  6c  4d  e  f  8
2r  3s  t  3
e.) r  2 s  4t  2
4 r  s  7t  8
f.)
5a  4b  3c  d  5e  2 f  34
2a  3b  8c  6d  e  4 f  38
6a  2b  7c  5d  3e  2 f  42
 5a  8b  5c  3d  9e  4 f  18