Matrices — Part 1: Order, types, equality, addition and subtraction: visual lesson, ICSE Class 10 Mathematics

Lesson

Matrices, Part 1

A matrix is a rectangular arrangement of numbers in rows and columns.

In this lesson you will

State the order of a matrix and classify it as a row, column, square, zero or identity matrix
Use equality of matrices to find unknown elements
Decide when two matrices can be added and add or subtract them
Multiply a matrix by a rational number and solve equations such as 2A + X = B

The same numbers as a matrix: $\begin{bmatrix} 30 & 18 \\ 25 & 22 \end{bmatrix}$, order $2 \times 2$.
Day	Idli	Dosa
Monday	30	18
Tuesday	25	22

Concept

What you will be able to do

State the order of a matrix
Recognise row, column, square, zero and identity matrices
Use equality of matrices to find unknowns
Add, subtract and scalar-multiply matrices
Solve equations such as $2A + X = B$

Concept

Rows, columns and elements

Each number in a matrix is an element. The element in row $i$ and column $j$ is written $a_{ij}$ : row first, then column. Matrices are named with capital letters and written inside square brackets.

Element positions in $\begin{bmatrix} 3 & -5 \\ 0 & 8 \end{bmatrix}$: row first, then column.
	Column 1	Column 2
Row 1	$a_{11} = 3$	$a_{12} = -5$
Row 2	$a_{21} = 0$	$a_{22} = 8$

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