Mr. Okenfuss

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Mr. Okenfuss
Sec. 3-5 3-6 Matrix Operations
Obj 3 Student will examine and solve linear
systems and matrices
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elements
The elements of a matrix are what separates each
matrix from another. They are the numbers that
are arranged neatly into rows and columns. Each
row and column stands for a specific
item. Thinking about football (as I often do)
and stats, lets look at Matt Leinarts stats over
his 3 years starting at U.S.C.
Year completions Attempts Yds. T.D.s
Ints 2003 232 368 3229 35
9 2004 269 412 3322 33
6 2005 275 424 3738 29
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These are typically kept in matrix form without
the knowledge of the fan or statistician just as
displayed earlier. We can modify that matrix and
put it in math form by eliminating the headings
and placing brackets around the information.
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rows/columns
The rows and columns as well as the elements help
define a matrix and make it unique. The rows
of a matrix move left to right and we can count
the rows by identifying the number of elements
down the left side. The columns of a matrix go
from top to bottom and can be counted by the
number of elements along the top edge of the
matrix.
Using our matrix from before of Matt Leinarts
stats we can count the rows and columns in that
specific matrix.
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The dimensions of a matrix are determined by the
number of Row and columns in a matrix, much like
a piece of lumber. Similar to a 2x4 is 2 tall
and 4 wide, a 2x4 matrix is 2 rows tall and 4
columns wide. So our Leinart matrix that had 3
rows and 5 columns is called a 3x5 matrix.
So the matrix A
is a 3x3 matrix
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Scalar multiplication
Scalar multiplication- is when you multiply each
element in a matrix by the same number. Using
the example from before

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In a typical college season, there are 12 regular
season games and one bowl game so all of
Leinarts stats are figured over 13 games. If we
would like to compare his stats to some of the
NFLs elite quarterbacks, we should project his
stats out over a 16 game season. To find out the
scaling factor we can solve this simple ratio
And x1.23 so if we multiply Leinarts stats by a
factor of 1.23, we would be able to project his
stats at U.S.C. out to the equivalent of a 16
game NFL season.
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So
1.23

Lets compare his years to those of Kurt Warner
in 1999 and Dan Marino in 1984, two of the most
prolific passing years to date
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Leinart
Which of these three premier quarterbacks had the
best season?