1. Matrices
A matrix is a rectangular array of numbers
arranged in rows and columns.
The dimensions of a matrix are written as
rows x columns.
Count AcrossCount
Down

2. Example
5 3
4 4
2 0
 
 − 
  
7 4 2
8 1 0
− 
 − 
This is a 2 x 3
matrix
This is a 3 x 2
matrix

3. Naming Matrices
A capital letter is used to name a matrix.
Each individual entry is named by its
position in the matrix.
11 12 13 14 15
21 22 23 24 25
31 32 33 34 35
a a a a a
a a a a a
a a a a a
 
 
 
  

4. Find a13, a24, and a33

5. Find a13, a24, and a33

6. Find a13, a24, and a33

7. Find a13, a24, and a33

8. Special Matrices
A matrix with the same number of columns
and rows (2 x 2, 3 x 3, etc.) is called a
square matrix.
A matrix with all zeros is called a zero
matrix.

9. Equal Matrices
Two matrices are equal if:
They have the same dimensions
The corresponding entries are equal
7 8
7 8
1
16 0.5 4
2
7 4
7 4
 
  
   =   
 −  − 
Each pair is equal:
7 = 7
8 = 8
½ = 0.5
Etc.

10. Using Equal Matrices
Equal matrices can be used to solve for
variables.
2
3 4 2
3 9 3
7 4 7 4
x y
z
+   
   =   
   − −   
Set up each equation
separately with
corresponding entries
3 = x
4 = y +2 (y = 2)
z2
= 9 (z =+3 or -3)

11. Try these

13. Scalar Multiplication
Matrices can be multiplied by a single
number called a scalar. In scalar
multiplication, multiply everything in the
matrix by that number.
2 6 6 18
3
4 1 12 3
   
=   − −   

14. Representing Points
Points can be represented in a matrix.
A matrix for the points (3,5); (-2,4); and (1,-1)
would look like this:
3 2 1
5 4 1
− 
 − 
x on the top
y on the bottom

15. Dilation
Multiplying a matrix of points by a scalar
represents a dilation of the figure.
(Dilations make the shape bigger or
smaller)

16. Example
What are the new coordinates if the this
triangle has a dilation factor of 3?
The new coordinates are (9,15); (-6,12); (3, -3)
3 2 1 9 6 3
3
5 4 1 15 12 3
− −   
=   − −   