4.1 & 4.2 Using Matrix Operations
Matrix: (Plural Form Matrices):
Dimensions of the matrix depend on the number of rows and columns.
Always read a matrix __________________ by _______________.
# Rows: ________
Dimension: ________
# Columns: _____
Numbers in the matrix are called entries. What is the entry in the 2nd row and
3rd column?
Different Types of Matrices
Name
Row Matrix
Column Matrix
Square Matrix
Zero Matrix
Example
Dimensions
4.1 & 4.2 Using Matrix Operations
Matrix Operations
Addition and Subtraction:
1. Matrices must have the SAME __________________.
2. Add or subtract the corresponding ________________.
Scalar Multiplication:
1. Multiply the constant OUTSIDE the matrix to EACH entry inside
the matrix.
Perform the indicated operations:
&6
5
1. $
%' 3 ' 2
' 2# &' 10 8
+
0 !" $%' 9 1
13 #
' 7 !"
Dimension of each matrix:_____
Dimension of the answer matrix:____
2.
Dimension of each matrix:_____
3.
Dimension of the answer matrix:____
=
Dimension of the answer matrix:____
4.
=
Dimension of each matrix:_____
Dimension of the answer matrix:____
4.1 & 4.2 Using Matrix Operations
Solve the following matrix for x and y:
5.
Matrix Multiplication
In order to multiply two matrices:
1. The number of____________ in the first matrix must match the
number of ____________ in the second matrix.
If A = m x n
Product of AB = A
x B
(m x n) x (n x p)
= ______
If B = n x p
Describe the matrix product of AB:
A.) A: 2 X 3 B: 3 X 4
B.) A: 3 X 2 B: 3 X 4
Matrix Multiplication by Hand
Multiply the following matrices:
1.) Find AB
Dim: _________ Dim:_________
2.) Find BA
Product Dim:______________
4.1 & 4.2 Using Matrix Operations
Use matrix operations in order to simplify the expression.
3.)
Find AB + BC
Verify the above two examples using a calculator, then use a calculator to
simplify the following expression.
1.) B (A + C)
HW: p. 203 # 16-18, 21, 25-26, 32, 36
p. 211 # 11-16, 17-19, 23-26
2.) BA + BC
4.1 & 4.2 Using Matrix Operations
Using the above heath care example to answer the following questions.
A company offers the health care plans in the above example to it’s employees. The
employees receive monthly paychecks from which health care payments are deducted.
Use the matrices in the above example to write a matrix that shows the monthly
changes in heath care payments from this year to next year.