1. Matrix Operations McDougal Littell Algebra 2
Larson, Boswell, Kanold, Stiff
Algebra 2: Applications, Equations, Graphs

2. 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=
[ ] 2 rows
[ ]
3 columns
Note: * The DIMENSIONS of matrix A are 2 X 3 (read “2 by 3” )
* The numbers in a matrix are its ENTRIES.
Ex.) The entry in the second row and third column is 5.

3. Multiplying Matrices If____ is an m X n matrix and _____ is an
n X p matrix, then the product ______is an
m X p matrix.
A * B = AB
m X n n X p m X p
Conclusion: The ______ of two matrices is defined iff the number of in A is _______to the number of in B.

4. Let’s Practice: Product defined?
State whether the product AB is defined. Explain.
Ex.) A: 3X4, B:4X5
Solution:
Ex.) A: 3X2, B:5X2

5. Properties of Matrix Multiplication
Let A,B, and C be matrices and let c be a scalar.
1.) Associative Property of Matrix Multiplication:
____(BC) = (AB) C
2.) Left Distributive Property:
A( _____ ) = AB + AC
3.) Right Distributive Property:
(A + B)___ = AC + BC
4.) Associative Property of Scalar Multiplication:
c(AB) = A( __B)

6. Finding the Product of Two Matrices
Ex.) Find AB if
A = [ ] and B = [ -1 3]
[ ] [ -2 4]
[ ]
Solution:
AB = [(-2)(-1) + (3)(-2) (-2)(3) + (3)(4)]
[(1)(-1) + (-4)(-2) (1)(3) + (0)(4) ]
[(6)(-1) + (0)(-2) (6)(3) + (0)(4)] =
_______________.

7. 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] =
[-1 0][2 1] ________________
Ex.) BA
Solution: BA = [1 -4][3 2] =
[ ][-1 0] ________________
NOTE: ________ DOES NOT EQUAL TO ________

8. 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.

9. Solutions to the Guided Practice Problems:
Note to the teacher: Include the solutions to the guided-practice problems.