Transcript Matrix

Lesson 12.1 – Adding and Subtracting Matrices
CHAPTER 12 - MATRICES
Take notes in your notebook.
Work the problems in your notebook
BEFORE advancing to the solutions.
A MATRIX
A
matrix is a rectangular
arrangement of numbers into
rows and columns.
4 -2
9
0 3 -5
This is a 2 by 3 Matrix.
A MATRIX
2 Rows and 3 Columns
4
0
-2
3
9
-5
VOCABULARY
 Matrix
- a rectangular array of variables or
numbers in horizontal rows and vertical
columns enclosed in brackets.
 Element
- each value in a matrix; either a
number or a constant.
 Dimension
- number of rows by number of
columns of a matrix.
 **A matrix is named by its dimensions.
FIND THE DIMENSIONS OF EACH MATRIX.
2
1. A = 
0

4
1 
2 
2. B =  
3 
 
4 
1
5 

8 

Dimensions: 3x2
Dimensions: 4x1
 0 5 3 1
3. C = 


2
0
9
6


Dimensions: 2x4
FIND THE DIMENSIONS OF EACH MATRIX.
8
0

 10
1
0
4
3
2 
 3
 2
1

 7
0
4
1
0

1
3
3 x 3 (or
square
matrix)
6
5 9
2
7
3
3x5

8
6 
 1
2x2

2  (aka: square matrix)
9
5 7
0
1x4
(aka: row matrix)
  9
7
 
0
 
6
4x1
(aka: column matrix)
DIFFERENT TYPES OF MATRICES
Column Matrix –
  9
7
 
a matrix with only one column.
0
 
Row Matrix –
6
 9 5 7 0 
a matrix with only one row.
Square Matrix –
a matrix that has the same number of rows and
columns.  1  1
0

2 
ADDING MATRICES
1.) -3 -2
5 -7
6 -8
-9 6
Add the corresponding
elements of each matrix.
ADDING MATRICES
To add two matrices, they must have the same
dimensions.
To add, you simply add corresponding elements.
 5
 3

 0
 3  2
4    3
7   4
1 
0 
 3
Working matrix
5  (2)  3  1 
   3  3
4  0 
 0  4
7  (3)
Answer Matrix
 3

 0
 4
 2

4 
4 
ADDING MATRICES
4
0
-2
3
2x3
9
-5
-1 0
3 7
2x2
Matrices can only be added if they have
the same # of rows & columns
ADDING MATRICES
 8 0 1 3   1 7
 5 4 2 9    5 3

 
=

5 2

3  2
8  (1)
07
 1 5
3 2
 5 5
43
23
9  ( 2)
=

7
0
7
7
4
5
5
7

Solution
matrix

Working
matrix
SUBTRACTING MATRICES
1.)

-3 -2
5 -7
6 -8
-9 6
Subtract the corresponding
elements of each matrix.
SUBTRACTING MATRICES
To subtract two matrices, they must have the same
dimensions. You simply subtract corresponding
elements.
Working matrix
 9 2 4   4 0 7   9 4
 5 0 6    1 5  4 

 
   5 1
 1 3 8   2 3 2  1  (2)

 5

 4
 3
20
05
33
47 

6  (4)
8  2 
Solution matrix
2
5
0
 3

10 
6 
SUBTRACTING MATRICES
=

2
8

 1
4
0
5
3 0
1


 7   3  1
0   4 2
Working matrix
2-0 -4-1
8-3
3-8
0-(-1) -7-1
1-(-4) 5-2
0-7

=
8

1
7 
Solution matrix
2 -5 -5
5 1 -8
5
3
-7

YOU TRY THESE
1.) -3 -2
5 -7
2.) 3 -7
7 -1
3.) -5 7
-3 -9
6 -8
-9 6
4 -3
7 8
-6 5
-1 7
YOU TRY THESE (SOLUTIONS)
1.) -3 -2
5 -7
2.) 3 -7
7 -1
3.) -5 7
-3 -9
6 -8
-9 6
4 -3
7 8
-6 5
-1 7
3 -10
-4 -1
7 -10
14
1
7
2
-2 -16
YOU TRY THESE
4.)
0 -3
-1 4
5.) 1 1
1 1
6.) -5 7
-3 -9
-6 0
3 1
4 -3
7 0
5 -7
3 9
YOU TRY THESE (SOLUTIONS)
4.)
0 -3
-1 4
5.) 1 1
1 1
6.) -5 7
-3 -9
-6
3
4
7
5
3
0
1
-3
0
-7
9
6 -3
-4 -2
-3 4
-6 1
0 0
0 0
CLASS WORK



Read Lesson 12.1 “Adding and Subtracting
Matrices” in your textbook and review the Power
Point lesson again.
Complete the 12.1 Vocabulary Worksheet
Review and complete the 12.1 Reteaching
Worksheet
HOMEWORK
In your textbook:
 Lesson 12.1/ 7- 17odd, 19-29
MATRIX LOGIC
Jim, Mario and Mike are married to Shana, Kelly and Lisa.
Mario is Kelly’s brother and lives in Florida with his wife.
Mike is shorter than Lisa’s husband.
Mike works at a bank.
Shana and her husband live in Kentucky.
Kelly and her husband work in a candy store.
Who is married to whom?
Jim
Shana
Kelly
Lisa
Mario
Mike
X
X
O
O
X
X
O
X
X