Introduction to Matrices

Matrices are a useful way to represent and manipulate data in order to model situations. The elements in a matrix can represent data, equations or systems and have many real-life applications.

What are matrices?

A matrix is a rectangular array of elements (numerical or algebraic) that are arranged in rows and columns
The order of a matrix is defined by the number of rows and columns that it has
- The order of a matrix with $m$ rows and $n$ columns is $m \times n$
A matrix $A$ can be defined by $A = (a_{i j})$ where $i = 1, 2, 3, . . ., m$ and $j = 1, 2, 3, . . ., n$ and $a_{i j}$ refers to the element in row $i$ , column $j$

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What type of matrices are there?

A column matrix (or column vector) is a matrix with a single column, $n = 1$
A row matrix is a matrix with a single row, $m = 1$
A square matrix is one in which the number of rows is equal to the number of columns, $m = n$
Two matrices are equal when they are of the same order and their corresponding elements are equal, i.e. $a_{i j} = b_{i j}$ for all elements
A zero matrix, $O$ , is a matrix in which all the elements are $0$ , e.g. $O = (\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix})$
The identity matrix, $I$ , is a square matrix in which all elements along the leading diagonal are $1$ and the rest are $0$ , e.g. $I = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})$

Examiner Tip

Make sure that you know how to enter and store a matrix on your GDC

Worked example

Let the matrix $A = (\begin{matrix} 5 & - 3 & 7 \\ - 1 & 2 & 4 \end{matrix})$

Write down the order of

A

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State the value of

a_{2, 3}

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Introduction to Matrices (DP IB Maths: AI HL)

Revision Note

Introduction to Matrices

What are matrices?

What type of matrices are there?

Examiner Tip

Worked example

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Author: Naomi C