Download Slide 1 - Walden University ePortfolio for Mike Dillon

Pre-Calculus – Chapter 2
Systems of Equations
It’s time to play…
Pre-Calc
Jeopardy
Rules for the Game
When it is your team’s turn, select a category and an amount.
After Mr. Dillon has finished asking the question, any team
may buzz in. If you buzz in early, you will not be called on.
If the team that buzzes in answers correctly, they get those
points and choose the next category.
If the team answers incorrectly, they lose the points. Mr.
Dillon will then re-read the question so the other teams can
have a chance to answer. A team is NOT obligated to answer
if they do not want to.
There will be a Final Jeopardy question at the end of the
game where teams can wager the points they have earned.
Any questions?
Today’s Categories
Solving Systems of Equations
Matrix Stuff
Augmented Matrices
Linear Inequalities
Linear Programming
The Answer is One
Solving
Systems
Matrix Stuff
Augmented
Matrices
100
200
300
400
500
100
200
300
400
500
100
200
300
400
500
Linear
Inequalities
Linear
Programming
The Answer is
One
100
200
300
400
500
100
200
300
400
500
100
200
300
400
500
Go to Final Jeopardy
100 Points
This method for solving
systems is the most visual
way to solve…
Graphing
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200 Points
This method for solving
systems involves replacing
expressions that are equal.
Substitution
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300 Points
This method for solving
systems ends with
“-limination.”
Elimination
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400 Points
This method for solving systems
of equations works great when
you have 3 or more equations and
3 or more variables.
Augmented Matrices
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500 Points
Solve the following system
of equations:
3x – 4y = 360
5x + 2y = 340
(80, -30)
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100 Points
Two matrices are equal if…
…they have the same dimensions and each
corresponding element is equal.
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200 Points
Suppose that A is a 3 x 2 matrix
and B is 2 x 3 matrix. Can you
determine A + B?
No. You can only add matrices with the
same dimensions.
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300 Points
Suppose that A is a 3 x 2 matrix
and B is 2 x 3 matrix. Can you
determine AB?
Yes. The number of columns in the first
matrix must equal the number of rows in
the second matrix.
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400 Points
2
A
3
Find AB:
4
 2 1 2
B




2
0 4 7 
4 18 32 
6 11 20


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500 Points
Find the inverse:
5 8
A

2 1
 1  1  8
A 


11  2 5 
1
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100 Points
This is one row operation
that can be used to
transform a matrix…
Interchange rows.
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200 Points
This is another row
operation that can be used
to transform a matrix…
Multiply a row by a scalar.
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300 Points
This is yet another row
operation that can be used
to transform a matrix…
Multiply a row by a scalar and add it to
the row (or a multiple of the row) that
you are replacing.
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400 Points
When simplifying a matrix, you
want this number in the
triangular area below the main
diagonal.
ZERO
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500 Points
Solve this system using a matrix:
x - 2y + z = 7
3x + y – z = 2
2x + 3y + 2z = 7
(2, -1, 3)
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100 Points
Use this type of line for the
boundary when the inequality is
less than or greater than.
DOTTED LINE
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200 Points
Use this type of line for the
boundary when the inequality is
less than or equal to or
greater than or equal to.
SOLID LINE
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300 Points
When solving a system of
linear inequalities, this is the
region of the graph where the
solutions are located.
Where the shaded parts of each graph
overlap.
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400 Points
This theorem states that the maximum
and/or minimum values of a function
constrained by a system of inequalities
will be located at the vertices of
polygonal region bounded by those
inequalities.
VERTEX THEOREM
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500 Points
Solve the following system of
inequalities:
y > 2x – 4
y ≤ -x + 5
See Mr. Dillon’s Sketch…
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100 Points
This is the first step in a
linear programming problem.
Define the Variables
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200 Points
This is the second step in a
linear programming problem.
Write the constraints in the form of
linear inequalities.
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300 Points
This is the third step in a
linear programming problem.
Graph the inequalities and find the
coordinates of the vertices.
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400 Points
This is the fourth step in a
linear programming problem.
Write a function to be maximized or
minimized.
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500 Points
These are the final two
steps in a linear
programming problem.
Substitute the ordered pairs to find the
values and select the max/min value.
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100 Points
In an identity matrix, this
number is found along the
main diagonal.
ONE
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200 Points
This is the number of
“rows” in a row matrix.
ONE
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300 Points
This is the number of
“columns” in a column
matrix.
ONE
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400 Points
Find the determinant of the
following matrix:
3 5
A

1 2
ONE
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500 Points
This is “NOW” spelled
backwards.
“WON”
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FINAL JEOPARDY
The category for Final Jeopardy is...
LINEAR PROGRAMMING
Write down your wager now.
Here is the question…
FINAL JEOPARDY
Open your books to page 95. Solve
question #18. You must show work
and your final answer is the amount
of “maximum revenue.”
Maximum Revenue: $170000
Pre-Calculus – Chapter 2
Systems of Equations
And the winner is…
Pre-Calc is fun
and easy!