Matrices — Part 1: Matrices, types and operations: visual lesson, CBSE Class 12 Mathematics

Lesson

Matrices, Part 1: Arranging numbers in rows and columns

A matrix is a rectangle of numbers that we can add, scale and multiply.

In this lesson you will

Write data as a matrix and state its order
Construct a matrix from a rule for its general element
Identify row, column, square, diagonal, scalar, identity and zero matrices
Use equality of matrices to find unknowns
Add, subtract, scalar-multiply and multiply matrices, and show that AB need not equal BA

The same data as the $2 \times 3$ matrix $\begin{bmatrix} 25 & 40 & 15 \\ 30 & 20 & 35 \end{bmatrix}$.
	Bats	Balls	Helmets
Branch P	$25$	$40$	$15$
Branch Q	$30$	$20$	$35$

Concept

What you will be able to do

Write data as a matrix and give its order
Build a matrix from a rule such as $a_{ij} = 3i - j$
Name the types of matrices
Use equality to find unknown entries
Add, scale and multiply matrices; see why $AB \ne BA$

Concept

What is a matrix?

A matrix is a rectangular arrangement of numbers (its elements or entries) in rows and columns, enclosed in brackets. We name matrices with capital letters.

S = \begin{bmatrix} 25 & 40 & 15 \\ 30 & 20 & 35 \end{bmatrix}

The same data as the $2 \times 3$ matrix $\begin{bmatrix} 25 & 40 & 15 \\ 30 & 20 & 35 \end{bmatrix}$.
	Bats	Balls	Helmets
Branch P	$25$	$40$	$15$
Branch Q	$30$	$20$	$35$

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