Download Matrix Operations - IISME Community Site

Matrix Operations
McDougal Littell Algebra 2
Larson, Boswell, Kanold, Stiff
Algebra 2: Applications, Equations, Graphs
Review:What is a Matrix?
•
•
Definition of Matrix: A rectangular arrangement of numbers in rows and
columns.
Ex): Matrix A below has two rows and three columns.
A=
[6
[-2
2
0
3 columns
-1 ] 2 rows
5 ]
Note: * The DIMENSIONS of matrix A are 2 X 3
* The numbers in a matrix are its ENTRIES.
Ex.) The entry in the second row and third column is 5.
(read “2 by 3” )
Multiplying Matrices
If A is an m X n matrix and B is an
n X p matrix, then the product AB is an
m X p matrix.
A
mXn
*
B
nXp
=
AB
mXp
Conclusion: The product of two matrices is
defined iff the number of columns in A is
equal to the number of rows in B.
Let’s Practice: Product
defined?
State whether the product AB is
defined. Explain.
• Ex.) A: 3X4, B:4X5
• Solution: Yes, the product is defined by definition of the
product of two matrices.
• Ex.) A: 3X2, B:5X2
• Solution: No, the product is not defined since the number
of columns of A does not equal the number of rows of B.
Properties of Matrix
Multiplication
Let A,B, and C be matrices and let c be a scalar.
1.) Associative Property of Matrix Multiplication:
A(BC) = (AB) C
2.) Left Distributive Property:
A(B + C) = AB + AC
3.) Right Distributive Property:
(A + B)C = AC + BC
4.) Associative Property of Scalar Multiplication:
c(AB) = A(cB)
Finding the Product of Two
Matrices
• Ex.) Find AB if
A = [ -2 3 ] and B = [ -1 3]
[ 1 -4 ]
[ -2 4]
[ 6 0]
Solution:
AB = [(-2)(-1) + (3)(-2)
[(1)(-1) + (-4)(-2)
[(6)(-1) + (0)(-2)
= [ -4 6]
[ 7 -13]
[-6 18]
(-2)(3) + (3)(4)]
(1)(3) + (0)(4) ]
(6)(3) + (0)(4)]
Finding the Product of Two
Matrices
If A = [3 2] and B = [1 -4], find each product.
[-1 0]
[2 1]
Ex.) AB
Solution: AB = [3 2][1 -4] = [7 -10]
[-1 0][2 1]
[-1 4]
Ex.) BA
Solution: BA = [1 -4][3 2] = [7
[2 1][-1 0] = [5
NOTE:
AB
2]
4]
DOES NOT EQUAL TO
BA
Guided Practice Problems:
• Note to the teacher: See section 4.2:
Multiplying Matrices on the McDougal
Littell Algebra II book. Choose the
appropriate guided-practice problems
for your students.
Solutions to the Guided Practice
Problems:
• Note to the teacher: Include the
solutions to the guided-practice
problems.