Matrices

Syllabus tag: Kenya CBC | Grade 9 Mathematics | Strand 2.0 Algebra | Sub-Strand 2.1 Matrices (8 Lessons)

Lesson objectives

By the end of this sub-strand, you should be able to:

• Identify a matrix and state its order.
• Determine the position of an element within a matrix.
• Add and subtract matrices of the same order.
• Multiply a matrix by a scalar and organise real data in matrix form.

Matrices

A shopkeeper records how many loaves and how many packets of milk each of two branches sold. That information naturally forms a grid.

A matrix is exactly that: numbers arranged in rows and columns inside brackets.

a) What a matrix looks like

The numbers inside are called entries. The brackets are part of the matrix, so always draw them.

b) Rows and columns

A row runs across. A column runs down.

The matrix above has two rows. The first is 4, 7, 2. It has three columns, the first being 4 and 1.

A simple way to keep them apart: a column is tall, like a pillar.

c) The order of a matrix

The order tells you the size. It is written as rows by columns.

Rows always come first. A 2 × 3 matrix is not the same shape as a 3 × 2 one.

d) Adding matrices

To add two matrices, add the entries that sit in matching positions.

The top left entries add to give the top left of the answer. Do the same for every position.

There is one condition. Both matrices must have the same order. A 2 × 2 matrix cannot be added to a 2 × 3 one. Some entries would have no partner.

e) Subtracting matrices

Subtraction works the same way, position by position.

Watch the order of subtraction, and watch the signs. In the bottom right, 3 − 8 gives −5, not 5.

The same condition applies. Both matrices must have the same order.

f) Using matrices for real information

Matrices are useful because they keep related figures together in one object.

Read this as two shops in the rows, and two products in the columns. Shop one sold 12 loaves and 8 packets of milk.

Next month's sales could be written as a second matrix of the same order. Adding the two would give the totals for both months.

g) Where this is used

A retail chain stores branch sales as a matrix. A school records marks by class and subject. Transport planners hold route distances the same way.

Words to know

• Matrix -- a rectangular arrangement of numbers in rows and columns, written inside brackets.
• Element -- an individual number within a matrix, identified by its row and column position.
• Order -- the description of a matrix as its number of rows by its number of columns.
• Scalar -- an ordinary single number used to multiply every element of a matrix.
• Null matrix -- a matrix in which every element is zero.

:::checkpoint Check yourself

1. What is the order of a matrix with 3 rows and 4 columns?
2. Which comes first when writing the order, rows or columns?
3. Why can a 2 × 2 matrix not be added to a 3 × 2 matrix?
4. Add the matrices [1 3; 2 0] and [4 1; 5 6]. :::

Bridge to practice

The exercises begin with identifying order and position, move through addition, subtraction and scalar multiplication, and finish with problems that ask you to interpret matrix results in context. Before attempting any combination, write down the order of each matrix involved and confirm the operation is defined; several of the questions below are designed to catch exactly that omission.