Matrices and Determinant – SS3 Mathematics Lesson Note (First Term)

A matrix is a rectangular array of numbers, quantities or expressions arranged in rows and columns. The order of a matrix tells its number of rows and columns. Matrices of the same order can be added or subtracted. Common types include the zero (null) matrix, the row matrix and the column matrix. Interchanging rows and columns gives the transpose.

Behavioural objectives

By the end of the lesson, students should be able to:

• Define a matrix
• 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.

What is a matrix?

Mode: whole class

Teacher’s role/activities: Probe the students’ knowledge of matrices. Based on their responses, lead 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 X, for convenience, we have:

(i) X =

(ii)

(iii) (6 4 2 1)

Students’ role/activities: The students identify or give more examples of matrices.

What are the order and types of matrices?

Order of a matrix

Mode: whole class

Teacher’s activities: Lead the students to identify the order and different types of matrices.

Types of matrices

Mode: whole class

Teacher’s activities: Lead the students to identify and mention different types of matrices.

• Null/zero matrix: a matrix in which every element is zero, e.g. 0 0 0 0 0
• Row matrix: a matrix with a single row of elements, e.g. (2 3 4)
• Column matrix: a matrix with a single column of elements.

Students’ activities: Get the students to interchange the rows and columns of matrices A, B and C above (called their transpose) and give the order of A^T, B^T and C^T.

How do you add and subtract matrices?

Mode: whole class

Teacher’s activities: Lead the students to add and subtract two matrices A and B.

Example: Given matrices A and B, find A + B, B + A and A – B.

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

Given that A =

and B =

Find A + B, B + A and A – B.

Evaluation

Mode: whole class

Teacher’s role: The teacher asks the students the following questions.

• 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 =

and Y =

find X + Y.

Students’ activities: The students solve the problems above while the teacher goes around to check their solutions.

Assignment

Given the matrices P =

and Q =

find:

1. P + Q
2. P – Q
3. Q – P

References

• New concept mathematics
• Multipurpose mathematics