Warm-up
Find the inverse of the function:
1) Y = 3x5
Solve the system:
2) 3x + 2y = 12
x+ y =3
9.1
Interesting Facts
• Venus is the only planet that rotates
clockwise.
• Jumbo jets use 4,000 gallons of fuel to
take off .
• On average women can hear better
than men.
• The MGM Grand Hotel of Las Vegas
washes 15,000 pillowcases per day!
• The moon is actually moving away from
Earth at a rate of 1.5 inches per year.
• In Australia, Burger King is called Hungry
Jack's.
• Mosquitoes are attracted to the color blue
twice as much as any other color.
• Jacksonville, Florida, has the largest total
area of any city in the United States.
• The largest diamond ever found was an
astounding 3,106 carats!
• A comet's tail always points away from the
sun.
• The lens of the eye continues to grow
throughout a person's life.
Finish Tests
When done, work on any
make up work
Now accepting work from
4/14 – 5/5
Topic:
Matrices (Chapter 2)
Key Learning(s):
Matrices are a tool for organizing data so that it
is easily manipulated. They can be used to
obtain additional information and to draw
conclusions about the data.
Unit Essential Question (UEQ):
How can matrices be used to draw conclusions
about a set of data?
Concept I (3.1):
Organizing data into matrices
Lesson Essential Question (LEQ):
How can statistical data be organized into
matrices?
Vocabulary:
Equal matrices
Concept II (3.2):
Adding and Subtracting Matrices
Lesson Essential Question (LEQ):
How do you determine corresponding
elements in a matrix?
Vocabulary:
Matrix addition
Matrix equation
Concept III (3.3):
Matrix Multiplication
Lesson Essential Question (LEQ):
How are the dimensions of a matrix related
to the ability to multiply matrices?
Vocabulary:
Scalar
Matrix multiplication
Concept IV (3.6):
Identity and Inverse Matrices
Lesson Essential Question (LEQ):
How would you describe the identity matrix
and its uses?
Vocabulary:
Square matrix
Identity matrix
Inverse matrix
§3.1: Organizing Data & Matrices
LEQ: How can statistical data be organized
into matrices?
Uses for matrices…
Math Toolbox p.107
Topics
• Organizing Statistical Data
• What is the difference between a 2x3
matrix and a 3x2 matrix?
• Presenting Data from a table in a matrix
• Elements, rows, columns (row, column)
• Equal matrices = iff same dimensions and
corresponding elements are equal
• Solving matrices with algebra involved
Practice
3.1 Worksheet
Finish 3.1 Worksheet
(Both Sides)
Section 3.1
P.104-105
#2 – 10 even
11 – 14, 16
11 - 22 even
Warm-up
5/6/08
On a separate sheet of paper
Do p. 143
# 1 – 6 all
Turn in when finished.
Interesting Facts
• The first condoms were made of linen.
• Cleopatra wasn't Egyptian; she was
Greek.
• Medical studies show that intelligent
people have more copper and zinc in
their hair.
• When you correct for weight
differences, men are proportionately
stronger than horses.
• More boys than girls are born during
the day; more girls are born at night.
• People in nudist colonies play
volleyball more than any other sport.
• Vultures fly without flapping their
wings.
• Apples are 25% air.
• Actor John Wayne made more than 200
movies.
• At their closest point, the Russian and
U.S. borders are less than two miles
apart.
Go over
Homework
Return Test
Papers
§3.2: Adding and Subtracting
Matrices
LEQ: How do you determine
corresponding elements in a matrix?
• Matrix addition/subtraction – add/subtract
corresponding elements
• Explain why you add matrices only if they
have the same dimensions.
• Is matrix subtraction commutative? Why?
• Matrix equation – addition/subtraction
properties of equality
Determinants/Systems
• http://www.tialgebra.com/activities/alge
bra_ii/265/#
Practice
3.2 Worksheet
Assignment
Section 3.2
p.111 – 112
#2 – 12, 32 - 38
Warm-up
5/7/08
On a separate sheet of paper,
Complete the following:
(for a grade)
p. 143
#7 – 10
Turn in when complete.
Take out homework & put on desk.
Interesting Facts
• Flamingos can only eat with their
heads upside down.
• Babies start dreaming even before
they're born.
• The word 'gymnasium' comes from the
Greek word gymnazein which means
'to exercise naked.'
• 4.5 pounds of sunlight strike the Earth
each day.
• 40 degrees Celsius is equal to -40
degrees Fahrenheit. Your brain is 80%
water.
• Your brain is 80% water.
• The phrase 'rule of thumb' is derived from
and old English law which stated that you
couldn't beat your wife with anything wider
than your thumb.
• It is illegal to mispronounce 'Arkansas'
while in the state of Arkansas!
• There are more than 1,000 chemicals in a
cup of coffee. Of these, only 26 have been
tested, and half caused cancer in rats.
• The Pittsburgh Steelers were originally
called the Pirates.
• Over 98 percent of Japanese people are
cremated after they die.
• The penguin is the only bird that can
swim, but cannot fly.
Check / Go over
3.2 Worksheet
Adding/Subtracting Matrices
10.3: Matrix Multiplication
LEQ: How are the dimensions of a matrix
related to the ability to multiply matrices?
Scalar Multiplication (Scalar)
You can also multiply two matrices.
Method:
 Multiply the elements of each row of the first matrix
by the elements of the first column of the second
matrix.
 Add the products.
Use scalar Multiplication
Follow along – example 2 p.115
Use a calculator to find the product
Practice
3.3 Worksheet
Quiz?
Assignment
Section 3.3
p.118
Use calculator: 30-38 Even
#2 – 18 Even
Warm-up
3.6
Find the product, if possible. If not, possible,
write product undefined.
1) [2]
[3 1 -2]
[1]
2) [1] [1 0]
[2] [0 1]
3) [-1 0 -2]
[1]
[2 3 1]
[3]
[2]
Did you know
• Persia changed its name to Iran in 1935.
• Rice flour was used to strengthen some of the bricks
that make up the Great Wall of China.
• Russia is the world's largest country with an area of
17,075,400 square kilometers.
• Seven asteroids were especially named for the
Challenger astronauts who were killed in the 1986
failed launch of the space shuttle.
• Soil that is heated by geysers is now making it
possible to produce bananas in Iceland.
• Some asteroids have other asteroids orbiting them.
• St. Paul, Minnesota was originally called Pigs Eye
after a man named Pierre "Pig's Eye" Parrant who set
up the first business there.
• Stalks of sugar cane can reach up to 30 feet.
• Tasmania is said to have the cleanest air in the
world.
• Thailand used to be called Siam.
• The Amazon rainforest produces more than 20%
the world's oxygen supply.
• The Angel Falls in Venezuela were named after an
American pilot, Jimmy Angel, whose plane got stuck
on top of the mountain while searching for gold.
• The Apollo 17 crew were the last men on the moon.
• The Chihuahua Desert is the largest desert in North
America, and is over 200,000 square miles.
• The Dead Sea has been sinking for the last several
years.
Go over 3.3 WS #1 – 35 odd
3.3 Summary
p. 144
#11 – 14
Turn In
§3.6: Identity and Inverse Matrices
LEQ: How would you describe the identity
matrix and its uses?
First, we need to know how to find the
determinant of a matrix
(kind of like an “answer”).
Math Toolbox p.134
#1-8
Identity Matrix
p. 135
• Find product: #1a, 1b?
• Find product: #3.
A square matrix is a matrix with the same
number of columns as it has rows.
The Identity matrix is a square matrix with 1’s
along the diagonal and 0’s everywhere else.
Inverse Matrix
• IF X is the inverse matrix of A, then
AX = I (A times its inverse = the identity)
Not all matrices have inverses.
If detA = 0, then A does not have an inverse.
If detA ≠ 0, then A does have an inverse.
http://www.algebra.com/algebra/homework/Matrices-and-determiminant/InverseMatrices.lesson
If A = [ a b]
[ c d]
Then, A-1 = *swap a & d, make b,c neg.
1
[d -b]
(det A) [-c a]
You can also use inverse matrices to solve
matrix equations.
[0 -4] X = [0]
[0 -1]
[4]
For this problem A-1 does not exist, so you
cannot solve the problem.
Examples
• 3-6 Worksheet
Assignment
Section 3.6
p.139-141
#2 – 18 Even
34 – 36 Even (Graphing Calculator)
Warm-up
5/9/08
Solve for x, y, and z (review of chapter 4).
-3x + 8y + 1z = -18
-2x – 6y – 9z = -15
-6x + 5y + 3z = 13
(-3,-4,5)
Interesting Facts
• In 2001, St. Patrick's Day was banned in
Ireland because of the scare caused by foot
and mouth disease.
• A 13-year-old boy in India produced winged
beetles in his urine after hatching the eggs in
his body.
• Airports that are at higher altitudes require a
longer airstrip due to lower air density.
• Amish people do not believe in the use of
aerosol air fresheners.
• Annually 17 tons of gold is used to make
wedding rings in the United States.
• Approximately 1 billion stamps are produced
in Australia annually.
• Being unmarried can shorten a man's life by
ten years.
• DC-10, the name of an airplane stands for
"Douglas Commercial."
• Every U.S. bill regardless of denomination
costs just 4 cents to make.
• Fires on land generally move faster uphill
than downhill.
• If someone was to fly once around the
surface of the moon, it would be equal to a
round trip from New York to London.
• In 1907, on New Year's Eve, the original ball
that was lowered in Times Square was made
of wood and iron and had 100 light bulbs on
it.
• Approximately 75% of human poop is
made of water.
• It has been estimated that the fear of the
number 13 costs Americans more than $1
billion per year!
• Smokers eat more sugar than nonsmokers do.
• Beavers can swim half a mile underwater
on one gulp of air.
• It takes twelve ears of corn to make a
tablespoon of corn oil.
• 10 of the tributaries flowing into the
Amazon river are as big as the Mississippi
river.
Reminders:
• All library books are due
by the end of today.
• Check your lockers, etc.
• Your final: 5/21 (last day)
Solving Systems with Matrices
Practice Worksheet on
solving systems
Matrices Review Sheet
Warm-up
5/12/09
1) Write two matrices whose product equals
I.
2) Write a 3x3 matrix. What are the
necessary properties that need to exist so
that matrices can be
 Added
 Subtracted
 Multiplied
Random Facts
• Baby beavers are called kittens.
• You have no sense of smell when you're
sleeping!
• Ants don’t sleep.
• An albatross can sleep while it flies!
• The earth is .02 degrees hotter during a full
moon.
• By feeding hens certain dyes they can be
made to lay eggs with multi-colored yolks.
• 40% of all indigestion remedies sold in
the world are bought by Americans.
• Animals will not eat another animal that
has been hit by a lightning strike!
• Dragonflies can travel up to 60 mph.
• The average 1 1/4 lb. lobster is 7 to 9
years old.
• Until President Kennedy was killed, it
wasn’t a federal crime to assassinate
the President.
• Each year, 24,000 Americans are bitten
by rats!
Test Reviews?
Go Over
3.6 Summary
p. 145
# 26 - 32
Word Problems
Handout of Word
Problems
HW: Study!
Warm-up
5/13/08
Some systems may not be able to be solved
using matrices (because they have no inv)
You may have to solve these matrices by
hand:
1) x + 4y = -19
-3x – 12y = 57
2) 2x + 2y = -4
x +y=0
Announcement
• Your “final” test will be on 5/21/08
• We will “review” and test on that day
• On Tuesday, you will only go to 1st
and 3rd block classes (they will both
be 3hrs long)
• On Wednesday, you will only go to 2nd
and 4th block classes
• You will not come to 4th block on the
20th.
Interesting Facts
• Crushed cockroaches can be applied to a
stinging wound to help relieve the pain.
• The average human body contains
enough iron to make a small nail.
• Astronauts cannot burp in space.
• A mole can dig a hole 300 feet deep in
one night.
• The sting from a killer bee contains less
venom than the sting from a regular bee!
• A rat can go without water longer than a
camel can.
• Cats cannot taste sweet things.
• A male baboon can kill a leopard.
• In its ancient form, the carrot was purple,
not orange.
• There are more fatal car accidents in July
than any other month.
• About 1 in 30 people, in the U.S., are in
jail, on probation, or on parole!
• Approximately 70,000 people in the U.S.
are both blind and deaf!
Check 8 – 10 on
Homework
Chapter 3 Test
Tomorrow:
Bring your Final Study
Guides to Class