Matrices and Determinant SS3 Further Mathematics Lesson Note

Specific objectives: At the end of the lesson students should be able to

• Define a matrices
• Identify a matrix 
• State the order and notation of matrices
• Mention and define types of matrices
• Add or subtract two or more matrices

INSTRUCTIONAL RESOURCES: Matrix charts, and matrix addition/subtraction charts. 

Step 1: identification of students’ prior ideas

Mode: whole class

Teacher’s Role/Activities: Probes the student’s knowledge of matrices. Based on the student’s responses, leads them to identify and define a matrix as a rectangular array of numbers, quantities, or expressions.

Examples

The composition of a class according to house and gender is shown below.

Calling the entries class as X, for convenience, we have

i       X    = 4 8            ii  2 ,4, -1          iii     (6 4 2 1)

                 6 6               3, 2, 6

                 8 2

                 10   11

STUDENTS ROLE/ACTIVITIES:

The students identify or give more examples of matrices

STEP2: Exploration Mode: whole class

Teacher’s Activities:

Lead the students to identify the order and different types of matrices.

 Step 3: Discussion

Mode: whole class

Teacher’s Activities: lead the students to identify and mention different types of matrices 

Null/Zero matrix: If zero matrix is a matrix in which every element is zero eg  0  0   0 0 0

Is a matrix with a single row of elements eg (2 3 4)

Column matrix: Is a matrix with a single column of element  

Students’ Activities: get the students to interchange the rows and columns of matrices A, B and C above (called their transpose) and give an order of AT   BT   CT

STEP iv: APPLICATION

Mode: whole class

Teacher’s activities: lead the students to operate the addition and subtraction of two matrices A and B.

Example: given that A =        B =   find A + B,   B + A is A-B

Students Activities: Allow the students to find from the example above B + A, B – A, and compare their results with A+ B, A-B. They should compute 

Given that   6 3 1   B= -1 3 4

             2 3 4      5 0 2

Find A+B,  B+A, c, A-B

Step V Evaluation

Mode: whole .class

Teacher’s Role: The teacher asks the students the following 

• Define a matrix 
• List 5 types of matrices, giving examples of each.
• State the order or notation of matrices 
• Is addition or subtraction commutative?
• Given that X = 0 – 1  y =  3  4

                                                2    3    -2 -1          find X + Y

Student Activities: The students solve the problems above while the teacher goes around to check their solutions.

Assignment: Given the matrices

• P  =   1  2   Q =  3  1  find P + Q

       0  2          0  3

• P – Q  
• Q – P

References: 

• New concept mathematics
• Multipurpose mathematics