Transcript 2 Matrix Supplement 2-2 - 2-3 and 2-5

2.2 and 2.3
More on arithmetic
Properties for addition
Identity Property:
There is a unique real number 0 such that
for every real number a
a + 0 = a and 0 + a = a
Prop. Of Opposites:
For every real number a, there is a unique
real number –a such that
a + (-a) = 0 and (-a) + a = 0
Property of the Opposite
of a Sum:
For all real numbers a and b
-(a + b) = (-a) + (-b)
Mishaps
• -4 + -4
• 4 - (-4)
• -(-4) + 4
• -(-4) – 4
• -(4 + 4)
How would you rewrite using the
communitive property?
4-3
200-(-300)
Subtraction is not communitive…you must convert
to addition by using the property of opposites!!!
What would be a great way to use Associative and
Communitive properties to do these mentally?
-16 + (-9) + 8 + 25
3.7 + 4.2 –x + y +6.3 + 12.8
-[24 + (-a)] + [-(-2 + a)]
Example
• A submarine descended to a level 230 m
below the surface of the ocean. Later, it
ascended 95 m and then dove 120 m. What
was the new depth of the submarine?
SAT score break down for 1997 and 1998
Year
Male
Female
Male
Female
1997
507
503
530
494
1998
509
502
531
496
Verbal
Math
Organize Data for the Verbal Portion
1997
1998
Male
507
509
Female
503
502
Organize Data for the Math Portion
1997
1998
Male
530
531
Female
494
496
Notice that when we
compare, they have
the same format!!!
Compare the overall SAT scores for the years
1997-1998 between girls and boys.
Organized Data for the Verbal Portion
1997
1998
Male
507
509
Female
503
502
Organized Data for the Math Portion
1997
1998
Male
530
531
Female
494
496
Totals
1997
1998
Male
Female
What are some things that need to be true in order to combine data?
Matrix:
• Table of numbers without the headers.
1997
1998
Male
507
509
Female
503
502
507 509


503
502


• Usually represented with capital letters.
507 509
A

503
502


• Classified by its dimensions: rows x columns
(m x n)
Find two matrices comparing Matinee and
Evening. Also determine the “total” matrix.
Theater
Children
Adult
Children
Adult
A
198
350
54
439
B
201
375
58
386
Matinee
Evening