1. St. Augustine Preparatory School September 21, 2015
Algebra II – Ch 3-5, 3-6
St. Augustine Preparatory School
September 21, 2015

2. Week Plan
Monday: Lesson 3-5 and 3-6 Tuesday: Lesson 3-4 Wednesday: In class assignment Thursday: Review (everyone participates) Friday: Review (If you are exempt, you may work on something else)

3. Real World Problems
You manage a clothing store and budget $6000 dollars to restock 200 shirts. T-shirts are $12, Polos are $24, and rugby shirts are $36 dollars. If you want to have twice as many rugby shirts as polo shirts, how many of each type should you buy? (Solution is on page 170 of your textbook)

4. Equations necessary
Let x = number of t-shirts Let y = number of polo shirts Let z = number of rugby shirts System: x + y + z = 200 z = 2y 12x + 24y + 36z = 6000 Answer: 20 tshirts, 60 polo shirts, 120 rugby shirts

5. Real World Problems
A stadium has seats. Seats sell for 25 dollars in section A, 20 dollars in section B, and 15 dollars in section C. The number of seats in Section A equals the total number of seats in B and C. Suppose the stadium takes in $1,052,000 from a sold out event. How many seats does each section hold?

6. Equations Necessary
Let a = number of seats in section a Let b = number of seats in section b Let c = number of seats in section c System: a + b + c = a – b – c = 0 (or a = b + c) 25a + 20b + 15c = Answer: a = b = c =

7. Chapter 3-6: Matrices
A matrix (plural: matrices) is a rectangular array of numbers that can be used to solve a system of equations Each number within a matrix is called a matrix element Matrix A is a “2x3 matrix” Ie. 2 rows, 3 columns

8. Questions
Page 172 question 21 and Page 173 question 49

9. Communicating Matrix Elements
We can describe certain numbers
in a matrix by the position of
the number.
The numbers that are the
subscript (like a12) are the
number of the row first and then
the column number. So a12 is the
first row and the second column
a11 = 2 a21 = 6
a12 = 4 a22 = 5
a13 = 1 a23 = 3

10. Representing a System with a Matrix
Place the following system into a matrix: a)
*Before you can put this into a matrix, b) all three equations must be in the form of x + y + z = 0. Each column must contain all x’s, y’s, z’s or constants.