Matrices – Part 1Learning Targets• I can find the dimensions of a matrix• I can add & subtract matrices• I can use scalar multiplication with matrices• I can multiply matrices

The information in this table can be displayed as a rectangular array of numbers enclosed by brackets, as shown.

Each number in a matrix is an element (or entry) of the matrix.

Such an array is called a matrix.

A matrix is usually named by a capital letter.

E =

This matrix is matrix E.

The dimensions of the matrix are the number of rows and columns.

This matrix has 2 rows and 4 columns, so its dimensions are 2x4.

When finding the dimensions of a matrix, you always write its rows first and columns second.

Row 1

Row 2

Column 1

Column 2

Column 3

Column 4

Examples: Find the dimensions of the matrices below.

1)

2)

3)

4)

sp se sw v

c

h

Sometimes it’s helpful to label the rows and columns to show us what they represent.

c h

sp

se

sw

v

The same information could be given by interchanging the rows and columns.

= E

= FMatrix F is called the transpose of Matrix E and is denoted by Et.

= F = Et

Suppose the EPA mandates that all of these fuel performance figures must increase 10% by next year.

This means that every element of matrix E must be multiplied by 1.10.

So, the resulting matrix is denoted by 1.1E.

1.1E =

1.1E =

This is called scalar multiplication.

Two matrices are equal if and only if they have the same dimensions, AND the elements in all corresponding positions (same row, same column) are equal.

In other words, they must be identical.

Example: Find the equal matrix.

a) b) c) d)

Two matrices having the same dimensions can be added (or subtracted) to produce a new matrix.

Examples:

1)

Two matrices having the same dimensions can be added (or subtracted) to produce a new matrix.

Examples:

1)

Two matrices having the same dimensions can be added (or subtracted) to produce a new matrix.

Examples:

3)

Matrix Multiplication

AA 2 x 3 BB 3 x 2A 2 x 3 B 3 x 2

To be able to multiply two matrices together, the two middle numbers of their dimensions MUST be equal.

The two outside numbers tell you the dimensions of your answer.

You Try: