This document discusses matrices and their use in representing inventory quantities of different book types (textbooks, fiction, non-fiction, reference) for two bookstores (Crazy Ken's Campus and Wacky Wally's College). It provides examples of representing the inventory quantities as matrices and using matrix addition to determine the total inventory of a company formed by merging the two bookstores. It also provides examples of scalar multiplication and evaluating matrix expressions.

1. What does this picture
have to do with matrices?
Matrix

2. http://ca.youtube.com/watch?v=xyAuNHPsq-g

3. A little warm up ...

4. A little warm up ...

5. http://matwww.ee.tut.fi/cgi-bin/matrix-algebra/MatrixAddition

6. Suppose that you have access to a woodworking shop in the
basement of Amos Hall where you make holiday toys for children as
an afternoon activity. Lately you have begun to sell your toys at a
local shop. You make four different kinds of toys, namely a train (t),
an airplane (a), a dragon (d), and a nameplate (n). Each of these
can be made very plainly out of pine (p), or with greater detail and
ornamentation out of oak (o). Let matrices O, N, and D represent
your sales for October, November, and December, as given below.

7. 1. State the dimensions of the matrices O, N, and D.
2. How many oak trains were made in December?
3. What does O2,4 represent?
4. How many of each item were sold for the entire three month period?
5. Construct a matrix S that contains entries representing the total
number of each item sold during the three months.

8. Crazy Ken’s Campus Bookstore’s inventory of books consists of the
following quantities.
Hardcover: textbooks—5280; fiction—1680; nonfiction—2320; reference—1890.
Paperback: textbooks—1940; fiction—2810; nonfiction—1490; reference—2070.
(a) Represent the inventory of Crazy Ken’s Campus Bookstore as a
matrix.
Wacky Wally’s College Bookstore’s inventory of books consists of
the following quantities.
Hardcover: textbooks—6340; fiction—2220; nonfiction—1790; reference—1980.
Paperback: textbooks—2050; fiction—3100; nonfiction—1720; reference—2710.
(b) Represent the inventory of Wacky Wally’s College Bookstore
as a matrix.

9. (c) Use matrix algebra to determine the total inventory of a new
company formed by the merger of Crazy Ken’s Campus
Bookstore and Wacky Wally’s College Bookstore.

11. Matrices and multiplication
... this is called quot;scalar multiplicationquot;
or quot;multiplication by a scalarquot;.

12. Now you try ...
without your calculator
with your calculator

13. Now put it all together ...

15. HOMEWORK
Solve for x:
Solve for x:
Solve for x:
Evaluate:
Evaluate:
Evaluate: